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Journal of the Learning Sciences
ISSN: 1050-8406 (Print) 1532-7809 (Online) Journal homepage: http://www.tandfonline.com/loi/hlns20
Friendships and Group Work in Linguistically
Diverse Mathematics Classrooms: Opportunities
to Learn for English Language Learners
Miwa Aoki Takeuchi
To cite this article: Miwa Aoki Takeuchi (2016) Friendships and Group Work in Linguistically
Diverse Mathematics Classrooms: Opportunities to Learn for English Language Learners, Journal
of the Learning Sciences, 25:3, 411-437, DOI: 10.1080/10508406.2016.1169422
To link to this article: https://doi.org/10.1080/10508406.2016.1169422
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Friendships and Group Work in
Linguistically Diverse Mathematics
Classrooms: Opportunities to Learn for
English Language Learners
Miwa Aoki Takeuchi
Werklund School of Education
University of Calgary
This ethnographic study examined students’opportunities to learn in linguisti-
cally diverse mathematics classrooms in a Canadian elementary school. I speci-
fically examined the contextual change of group work, which influenced
opportunities to learn for newly arrived English language learners (ELLs).
Based on analyses of video-recorded interactions, this study revealed a shift in
these ELLs’opportunities to learn from when they worked with teacher-assigned
peers to when they worked with friends. In both settings, ELLs tended to be
positioned as novices. However, when working with friends, they accessed a
wider variety of work practices. In friend groups, ELLs were occasionally
positioned as experts and had more opportunities to raise questions and offer
ideas. In contrast, when working with teacher-assigned peers, ELLs tended to
remain in the position of being helped. In some teacher-assigned groups, inter-
actions were characterized as authoritative, and ELLs’contributions and ideas
were rejected or neglected without relevant justifications or mathematical
authority established by their peers. The findings contribute to ongoing discus-
sions on group work and friendship in linguistically diverse classrooms.
Correspondence should be addressed to Miwa Aoki Takeuchi, Werklund School of Education,
University of Calgary, 2500 University Drive NW, Calgary, AB, T2N 1N4, Canada.
E-mail: miwa.takeuchi@ucalgary.ca
Color versions of one or more of the figures in the article can be found online at www.tandfonline.
com/hlns.
JOURNAL OF THE LEARNING SCIENCES, 25: 411–437, 2016
Copyright © Taylor & Francis Group, LLC
ISSN: 1050-8406 print / 1532-7809 online
DOI: 10.1080/10508406.2016.1169422
Group work and pair work have been implemented across disciplines as a tool for
providing rich academic and social learning opportunities to students. For example,
in its Principles and Standards for School Mathematics, the National Council of
Teachers of Mathematics (2000) outlined the importance of group work for com-
municating, explaining, and justifying mathematical ideas among learners. Group
work can also be a tool to enhance students’opportunities to discuss with and learn
from each other and to improve their social relationships (Cooper & Slavin, 2001).
Previous studies on group work demonstrated that students who engage in elabo-
rated explanations and participate in discussions tend to gain more opportunities to
learn mathematics (Chizhik, 2001; Webb, 1985). Despite the benefits of group work
for learning and socialization, however, researchers have raised concerns regarding
the imbalance in learning opportunities that might arise among students with
different social backgrounds during group work (e.g., Chizhik, 2001;Cohen,2004).
This study examines the relationship between group work and friendship in a
linguistically diverse school. Because of global mobility, schools in many countries
are facing issues stemming from their linguistic and cultural diversity. For example,
in Toronto, the largest city in Canada, where this study took place, 45% of the entire
population has a first language other than English or French, the official languages
(Statistics Canada, 2012). In relation to this growing linguistic diversity, equal access
to high-quality mathematics learning opportunities for all learners has been recog-
nized as an important issue (Diversity in Mathematics Education Center for Learning
and Teaching, 2007).
This article presents an ethnographic video-based study of group work in Grade 4
mathematics classrooms in a school where more than half of the students spoke first
languages other than English, the language of instruction. I examined students’
opportunities to learn in friend groups and teacher-assigned groups by analyzing
video data on group work interactions involving newly arrived English language
learners (ELLs) who were receiving English as a second language (ESL) instruction.
As described in detail in “Data Sources and Analytic Methods,”friendship in this
study is defined in two layers: (a) being stable playmates during recess and (b)
selecting each other as group members when a choice is given.
In this study, I address the following research question: How do newly arrived
ELLs’opportunities to learn differ between student-selected friend groups and
teacher-assigned groups? As elaborated further in the subsequent sections, this
study draws from the sociocultural theory of learning and conceptualizes opportu-
nities to learn as access to classroom mathematical discourse practices and access to
identities as a competent participant in the community (Esmonde, 2009;Gresalfi&
Cobb, 2006). The principal findings of this study suggest that newly arrived ELLs
accessed a wider range of opportunities to learn when friendships were established
among the group members. Specifically, ELLs tended to offer more ideas, engage in
more discussions, and be positioned as competent participants in friend groups. The
interactional analysis revealed power imbalances when ELLs were grouped with
412 TAKEUCHI
teacher-assigned partners who either were considered more advanced in mathe-
matics or played a leader role in the classroom. In these teacher-assigned groups,
ELLs tended to be positioned as novices and did not actively engage in discussion
with peers. Given that providing and receiving elaborated explanation can lead to
better learning opportunities for both mathematics learning (Webb, Farivar, &
Mastergeorge, 2002) and language learning (Swain, 2001), and gaining an identity
as a competent learner is an essential aspect of learning, ELLs gained richer
opportunities to learn in friend groups. As reviewed in the following section, the
current study advances the discussion on group work, particularly regarding two
topics: (a) linguistic diversity and group work and (b) friendships and power
dynamics in group work.
Linguistic Diversity and Group Work
In second language education, the quality and number of interactions available
during group work have been examined in relation to students’linguistic proficiency
development (Liang, Mohan, & Early, 1997;Swain,2001). In addition, patterns of
member relationships have been examined in relation to language learning oppor-
tunities (Storch, 2002). When focusing on the participation of ELLs or linguistic
minority students, previous studies have suggested that their contributions tend to be
devalued during group work across different education levels, from higher education
(Leki, 2001;Morita,2004)togradeskindergarten–12 (Kanno & Applebaum, 1995;
Too hey & Day, 1999). For example, Toohey and Day’s(1999) study on classroom
interactions described how subtle power imbalances in group work can hinder ELLs’
opportunities to contribute to the process and product of group work. Overall, these
studies have shown that linguistic minority students tend to remain in marginalized
positions during group work and internalize the perception that they are less
competent members of the group.
The inequity in learning opportunities can be challenged with a well-designed
pedagogical intervention. Previous studies on a particular group work pedagogy,
complex instruction, have shown the possibility of balancing inequities among
students with different statuses and identities (Boaler, 2006; Cohen, Lotan, &
Holthuis, 1997; Lotan, 2007). Complex instruction suggests a group work
pedagogy including respecting multiple abilities, assigning group-worthy open-
ended tasks, distributing roles, being explicit about students’responsibilities, and
maintaining shared accountability (Boaler, 2006). Focusing on linguistic diver-
sity, Bunch (2006) found that ELLs who presented fluent conversational profi-
ciency but limited academic proficiency were able to better integrate into group
work under complex instruction. These studies altogether demonstrate the sig-
nificance of attending to contexts and power dynamics in group work. The
current study pays careful attention to students’friendship as one of the salient
contexts affecting ELLs’engagement in group work.
FRIENDSHIPS AND GROUP WORK 413
Friendships and Power Dynamics in Group Work
The influence of friendship on collaboration during group work has not yet been
extensively examined across pedagogical contexts, tasks, and students’ages, and
previous studies have presented mixed findings. On the one hand, collaboration
among friends is reported to be more meaningful, preferable, and productive
compared to collaboration among non-friends, because friends tend to know their
similarities to and differences from other group members, have a strong commit-
ment to one another to maintaining an amicable relationship, and feel more
secure in working with one another (Azmitia & Montgomery, 1993; Fonzi,
Schneider, Tani, & Tomada, 1997; Hanham & McCormick, 2009; Strough,
Berg, & Meegan, 2001; Zajac & Hartup, 1997). Students also reported a pre-
ference for working with friends of the same gender identity (Strough et al.,
2001). During interactions in groups, friends tended to make more proposals and
spend more time on discussion (Fonzi et al., 1997). Consequently, friend groups
were reported to lead to more productive problem solving (Zajac & Hartup,
1997).
On the other hand, studies have reported that students prefer to work with
assigned partners. For example, some students feel pressured to choose their
friends, even when friends do not work well with one another (Mitchell, Reilly,
Bramwell, Solnosky, & Lilly, 2004). Kutnick and Kington (2005) reported that
girls working with friends achieved higher performance on tasks during group
work, whereas boys achieved lower performance with friends compared to non-
friends. It is reasonable to consider that the inconclusive nature of studies on
friendship and group work may stem from the interrelated influence of various
aspects of students’identities, tasks, and the classroom environment. Students
reported that friendship is a complex relationship and that layers of social
identities could affect collaboration during group work (Esmonde, Brodie, Doo-
kie, & Takeuchi, 2009).
Because friendships in school are dynamic and fluid (Faircloth & Hamm,
2011), treating friendships as an isolated variable will not necessarily generate
an ecologically valid account. Students’friendship formation can change over
time and can be affected by classroom learning experiences, especially experi-
ences in group work. The very process of group work can impact friendship, as
revealed in studies conducted in racially heterogeneous classrooms (Cooper &
Slavin, 2001; Slavin & Cooper, 1999). In addition, friendships can be inter-
related with other aspects, such as students’achievement, motivation, or per-
sonalities, and the way in which friendships influence group work can be
affected by the social organization of the classroom (Beaumont, 1999). Thus,
an ethnographic approach such as the one chosen for the current study is
beneficial for capturing the complexities of the classroom and the relationship
between friendship and group work.
414 TAKEUCHI
IDENTITY AND LEARNING IN SOCIOCULTURAL THEORY
Group work, which utilizes collaboration among peers, has been largely influenced
by Vygotsky’s(1978) theory of the zone of proximal development, which highlights
the distance between the level of a learner’s independent problem solving and the
level determined through problem solving in collaboration with peers and under
appropriate guidance. It sheds light on the buds of development, namely, the
prospective development of a learner that can bloom through collaboration with
others. The sociocultural theory of learning, based on Vygotsky’s theory, emphasizes
that learning is not an individual possession. Rather than reducing learners to passive
recipients of a body of factual knowledge, sociocultural theory emphasizes a dialec-
tical unity of learning and development and “comprehensive understanding invol-
ving the whole person”(Lave & Wenger, 1991, p. 33). Conceptualizing learning as a
process involving a change of identity is particularly relevant for an examination of
group work, in which students simultaneously engage in “a content space (consisting
of the problem to be solved) and a relational space (consisting of the interactional
challenges and opportunities)”(Barron, 2003,p.310).
To frame the concept of identity, I draw from the central tenet of sociocultural
theory, which pays close attention to different time scales and multiple levels of
history in development (Lemke, 2000; Saxe & Esmonde, 2005; Scribner, 1985).
In emphasizing the multiplicity of identity, Holland, Skinner, Lachicotte, and
Cain (1998) conceived of “persons as composited of many, often contradictory,
self-understandings and identities, whose loci are often not confined to the body
but spread over the material and social environment, and few of which are
completely durable”(p. 8). By considering identity as working across different
time scales, Wortham (2006) described how social identification during class-
room microinteractions came to focus on certain students’sociohistorical iden-
tities and shaped these students’academic trajectories at school. For example,
Wortham’s study demonstrated how two students were gradually identified
according to sociohistorical models of identities through a locally constructed
version of participant examples.
Conceptualizing identities on multiple time scales can help to capture the reality
of the classroom, where students negotiate and develop different scales of identities.
In this study, I focus on locally constructed social identity and positional identity in
relation to students’learning during group work. Through the lens of locally
constructed social identity, I examine identities such as “ELLs,”“students who are
adept at mathematics,”and “students who can speak ELLs’first languages and can
thereby help these students.”These social identities are reinforced by the way in
which the school, classroom, and teacher’s assessments and observations are struc-
tured and may have prolonged effects over several months or even beyond the
academic year. Positional identity is “the day-to-day and on-the-ground relations of
power, deference and entitlement, social affiliation and distance—with the social
FRIENDSHIPS AND GROUP WORK 415
interactional, social relational structures of the lived world”(Holland et al., 1998,p.
127). Positional identity sheds light on the moment-by-moment negotiation of a
position actualized through “access to spaces, activities, genres and through those
genres, authoritative voices, or any voice at all”(p. 128). In this study, I examine
students’interactions and the positional identities that they play during group work.
This study does not analyze participants’reports of self-understanding or expla-
nations of their identities. Instead, students’agency to negotiate their positional
identities is examined in the way they choose their group members when they are
given a choice. This methodological decision is motivated by my concerns about the
relationship between opportunities to learn and the power that is circulated through
social relationships and social classification (Wortham, 2006).
SETTING
This ethnographic video-based research was conducted in an urban elementary school
in a large school district in Ontario, Canada. The language of instruction of this school
was English, and the students began to learn French during Grade 4. The school had
approximately 450 students, with more than 30 different language groups represented;
23% of the students had been born outside Canada, and for approximately 53% of the
students, English was not the language spoken in their homes. Students’home
languages varied; the major home languages other than English included Bengali,
Cantonese, Farsi, French, Romanian, Russian, Spanish, Mandarin, Tamil, Urdu, and
Vietnamese. Each regular class in the school had 15–20 students. I conducted parti-
cipant observation in two Grade 4 mathematics classes taught by Ms. Sally Wilson.
1
The school offered ESL programs for students who were new to Canada (less than
2 years since their arrival) and whose English language proficiency was developing.
2
This study focused on four newly arrived immigrant students who were receiving
ESL support at the school and attending ESL classes during language and social
studies classes. In my analysis, I focused on four participants, Ajmal, Daniel, Karim,
and Sabina, who were the only students considered eligible for ESL programs at the
school at the time of the study. They were eligible because they had come to Canada
less than 2 years before the study was conducted and because they had limited
English language learning opportunities at home or in their home countries.
Ajmal and Karim came from Afghanistan and spoke Farsi as their first language,
Sabina came from Bangladesh and spoke Bengali as her first language, and Daniel
came from Mexico and spoke Spanish as his first language. Before coming to the
school, Daniel had lived in Québec, a French-speaking province, where he had
1
All participant names are pseudonyms.
2
Even though many students were considered to be ELLs in a broader sense, newly arrived
students who were receiving ESL instruction were called “ELLs.”Sometimes teachers called them
“ESL students.”
416 TAKEUCHI
received school education in French. Sabina was a girl, and Ajmal, Daniel, and
Karim were boys.
Context of Group Work
In Ms. Wilson’s classroom, group work was used daily for mathematics teaching.
She used group work among full-class discussions, word problem solving, project-
based learning, and hands-on activities. A variety of tasks were used for group work,
with some tasks categorized as being accountable to individuals and others to the
group. Some of the tasks had multiple solutions, and others had one correct answer.
In an interview, Ms. Wilson described her goal of using group work as follows:
I wanted them to talk about the math. So, if they’re talking about math, they’re
learning from each other; they’re having an opportunity to discuss it to use, hope-
fully, the vocabulary that’s been introduced or that they have prior knowledge of.
And then that will help them to start to form their own ideas and make connections.
As this quote suggests, Ms. Wilson used group work to increase opportunities
for students to talk, discuss ideas with each other, and use the mathematics
vocabulary they were learning. In addition, she used group work to help students
formulate their ideas and make associations through discussion with other students.
In terms of the teacher’s grouping strategy, at the beginning of the year Ms.
Wilson tended to assign students to groups. In assigning groups, Ms. Wilson
grouped Ajmal, Daniel, Karim, and Sabina with students who were perceived as
“being mathematically adept,”being “multilingual,”“exhibiting leadership,”and
“caring.”As suggested in the following excerpt from an interview with Ms.
Wilson conducted at the beginning of the academic year, these groupings were
intended to support ELLs who struggled to communicate in English:
I am hoping to get them working with classmates—I mean, working with some-
body in the class I know who has good mathematical understanding but will help
them to learn the math as well. But it’s a double-edged sword because I’m worried
that, instead of really learning math, they just sort of copy or go along with what the
other student has—not really understanding the math.
Ms. Wilson also allowed students to choose their own group members later in the
year and sometimes switched between two types of grouping depending on the
students’attendance and desk arrangement. Thus, there were periods when teacher-
assigned groups and student-selected groups co-occurred during the same period of
time. This unique context allowed me to examine newly arrived ELLs’opportunities
to learn in both settings, especially by examining how their opportunities to learn
varied between friend groups and teacher-assigned groups in the same month.
FRIENDSHIPS AND GROUP WORK 417
Generally speaking, newly arrived ELLs’academic language proficiency develop-
ment requires a minimum of 5 years (Cummins, 2000). Thus, I also included
interactions from different months within the academic year for my analysis.
DATA SOURCES AND ANALYTIC METHODS
This study drew from ethnographic data on group interactions in mathematics classes
over an academic year. Video data and field notes on cooperative group interactions
and audio-recorded interview data with the teacher were the main sources of data. The
previously described lens of sociocultural theory was also influential in the design of
this study in framing the reciprocity between identity and learning, which is manifested
through the relationship between friendships and group work.
The analysis focused on four ELLs’opportunities to learn in teacher-assigned
groups and friend groups. The ELLs’friends were identified through the analysis
of field notes taken during recess that recorded, for example, the games the
students played and with whom they spoke. If I observed two or more students
playing and talking together during recess for more than 3 weeks, and if they chose
each other for group members, I categorized them as friends. Although this method
does not leverage student interviews or questionnaires, it can offer ethnographic
insights into students’friendship formation.
The total of 45 hr of video data were collected over an academic year; however,
the analysis focused on the segments of video that captured group work in which
focal students were involved. Because group work was the mainfocus of this study, I
did not use the videos of whole-class discussions, teacher lectures, or individual
work. Ultimately, 20 hr of video were selected as the major data source for this study.
Students’work and classroom artifacts were analyzed as supplementary data.
As a first step of analysis, for each video-recorded lesson, I wrote a detailed
narrative of group work by focusing on the tasks completed by the groups, the
artifacts the students used, and the groups’conversations. I then separated each
narrative into episodes that were identified as the phases of collectively completing
tasks. For example, when the students worked together on a word problem involving
addition, phases of collectively completing tasks could include comprehending the
word problem, proposing solution(s) and equation(s), solving the equation, and
writing the solution. I identified all different phases of collectively solving word
problems as separate episodes. I excluded episodes during which the teacher stopped
by and provided a lecture for a small group (rather than simply checking on how the
students were working in their groups) to analyze students’dynamics. Thus, in total,
I analyzed 77 episodes. For the analysis of group work processes, I transcribed the
segments of the interactions, focusing on both the content ofthe conversation and the
participants’actions (e.g., pointing to the picture on a worksheet, flipping through a
notebook). The coding and descriptive quantitative analysis were completed using
418 TAKEUCHI
the data analysis software MAXQDA. Fisher’s exact test was used to compare
students’interactions between the two types of groups.
Analysis Procedures for Group Work Interactions
The analyses of interactions during group work entailed two steps. First, in order to
obtain a broad picture of the relationships and identities that students constructed
during group work, I referred to the coding schemes developed by Esmonde (2009)
on work practices and positional identities. The code for work practices was used to
characterize interactional patterns that students constructed during group work, and
the code for positional identities was used to describe the power dynamics that
students constructed during group work. I added the dimension of social authority
(not necessarily mathematical authority) to the coding scheme I used (Storch, 2002).
The coding scheme for work practice is summarized in Table 1.
The code for positional identities was used only when a power imbalance was
observed among group members with reference either to their competence or to
other forms of authority. By using the codes summarized in Table 2, I analyzed
episodes in which newly arrived ELLs were positioned with respect to compe-
tence in relation to their peers or to a particular knowledge or task.
In order to calculate interrater reliability, I randomly selected 12 episodes out of
the 77 coded episodes (15% of the entire coded episodes) from different periods in
the academic year. I recruited another coder who was not involved in data
collection and hence did not know which students were considered to be friends.
To compute interrater reliability, I used Krippendorff’s(2004) alpha. The coding of
both work practice and positional identities showed high interrater reliability. For
the work practice coding, the agreement rate was 83.3% (Krippendorff’sα=.771).
For the positional identities coding, the agreement rate was 91.7% (Krippendorff’s
α= .88). After a subsequent discussion with the other coder, I came to understand
that disagreement occurred largely because we paid attention to different aspects of
interactional details. For example, the other coder coded a work practice as helping
based solely on the student utterance “Can I help you with this?”However, I coded
the same episode as authoritative by paying attention to the subsequent interac-
tions, in which one student was forced by another student to erase his written work.
Subsequent discussion was held until the two coders came to an agreement.
Second, I focused on the process of group work by examining student interac-
tions. In the subsequent Results section, I present excerpts of interactions from the
most frequently occurring patterns of work practices and positional identities in
friend groups and teacher-assigned groups. In addition, I present interaction patterns
observed uniquely in both types of groups. In analyzing the video-recorded interac-
tions, I focused on the types of mathematics and language learning opportunities
available to ELLs. Specifically, I analyzed tasks that were undertaken by ELLs, types
of questions and responses, and who shared ideas and how.
FRIENDSHIPS AND GROUP WORK 419
TABLE 1
Coding Scheme for Work Practices
Work Practice Definition Example
Individualistic “A propensity for working
individually before consulting one
another, for not asking for help
when needed, and for denying help
to group members who expressed
confusion or requested assistance”
(Esmonde, 2009, p. 256).
In addition, if a student was
excluded from group interaction,
I coded it as an instance of
individualistic work practice.
Sabina (an ELL) and Cathy are both
writing down conclusions based
on the survey they have
conducted. They are sitting next to
each other but working
individually, without talking.
Cathy leaves Sabina to ask the
teacher questions.
Collaborative “Group members put their ideas
together, worked together, and
seemed to act as ‘critical friends’
when considering one another’s
ideas. Rather than quickly
accepting or rejecting one
another’s idea, collaborative
groups discussed and critiqued
ideas put out onto the public floor”
(Esmonde, 2009, p. 256).
Jasmine and Sabina (an ELL) are
working on a word problem.
Jasmine reads the problem aloud
while Sabina is looking at the
problem. Once Jasmine finishes
reading aloud, Sabina takes out a
calculator and suggests adding
some of the numbers in the
problem.
Helping “Mathematical talk was
asymmetrically organized, in which
one or more students instructed
other students about what to do”
(Esmonde, 2009,p.256).
Iris and Ajmal (an ELL) are working
on textbook problems. Iris
completes the problem earlier than
Ajmal does. Looking at Ajmal’s
notebook, Iris asks him to mark all
of the numbers in a stem-and-leaf
graph. Iris then shows him an
example of how to mark the graph.
Ajmal starts working quietly while
Iris waits for him to complete his
task.
Authoritative Students with social authority (but
not necessarily mathematical
authority) dominated the
conversations and held the power
to assign tasks or to decide the
correctness of ideas (Storch,
2002).
Karim (an ELL) and Naomi are
creating a survey sheet. While
examining Karim’s work, Naomi
repeatedly asks him, “Can I help
you with this?”Karim does not
respond but continues working.
Eventually Naomi takes away his
survey sheet, starts to erase what
he has written, and rewrites it.
Note. ELL = English language learner.
420 TAKEUCHI
RESULTS
Work Practices and ELLs’Positional Identities in Friend Groups and
Teacher-Assigned Groups
This section presents the findings on work practices and ELLs’positional identities
during group work in friend groups and teacher-assigned groups. As summarized
in Tab le 3, when I focused on work practices, helping work practice was most
frequently observed in both groups. In other words, during group work, students
were often seen helping each other to complete tasks or to understand particular
concepts, formulas, and definitions of terms. There was a significant association
between students’work practices during group work and types of groups (p=.015,
two-tailed Fisher’s exact test). A total of 27.5% of the episodes in friend groups
TABLE 2
Coding Scheme for Positional Identities
Positional Identity Definition Example
Expert “A group member who was
frequently deferred to
(mathematically) and who was
often granted authority to decide
whether his or her own and other
students’work was correct”
(Esmonde, 2009, pp. 257–258).
Iris, Laura, and Daniel (an ELL) are
designing a survey. Iris gives
Daniel instructions on how to
create a survey. She takes out the
paper he is holding and starts
writing down the example survey.
Daniel grabs the paper and starts
writing down something on his
own. Iris examines his work.
Expert: Iris
Novice: Daniel
Novice “A student who deferred to an expert
(positioning himself or herself as
less competent) and whose
opinion was frequently passed
over in discussions of
mathematical controversies
(positioned by others as less
competent)”(Esmonde, 2009,
pp. 257–258).
Dominant A group member who dominated the
conversation without presenting
any validation of mathematical
competence or knowledge (Storch,
2002).
Karim (an ELL) and Naomi are
creating a survey sheet. While
examining Karim’s work, Naomi
repeatedly asks him, “Can I help
you with this?”Karim does not
respond but continues working.
Eventually Naomi takes away his
survey sheet, starts to erase what
he has written, and rewrites it.
Dominant: Naomi
Subordinate: Daniel
Subordinate A group member who followed
instructions or orders without
questioning the dominating
students’authority (Storch, 2002).
Note. ELL = English language learner.
FRIENDSHIPS AND GROUP WORK 421
were categorized as collaborative, whereas 5.4% of the episodes in teacher-
assigned groups were collaborative. Students tended to work together and discuss
each other’s ideas when working with friends. Authoritative work practice was
observed only in teacher-assigned groups. In authoritative work practice, students
did not engage in meaningful discussions. It is noteworthy that few off-task work
practices were observed and that there were more off-task conversations in teacher-
assigned groups than in friend groups.
The findings on ELLs’positional identities during group work were crucial for
distinguishing between two different types of helping work practices: ELLs being
helped by others and ELLs helping others. Ta ble 4 summarizes the number of episodes
at the intersection of the particular positional identities of ELLs and the work practice.
TABLE 3
Work Practices in Friend Groups and Teacher-Assigned Groups
Work Practice n %
Friend groups
Off task 1 2.5
Authoritative 0 0
Helping 18 45
Collaborative 11 27.5
Individualistic 10 25
Total 40
Teacher-assigned groups
Off task 4 10.8
Authoritative 3 8.1
Helping 15 40.5
Collaborative 2 5.4
Individualistic 13 35.1
Total 37
TABLE 4
The Intersection of Positional Identities of Focal English Language Learners and Work
Practices in Friend Groups and Teacher-Assigned Groups
Positional Identity
Work Practice In Between Novice Expert Subordinate
Friend groups
Helping 13 4
Collaborative 1 4
Individualistic 3
Teacher-assigned groups
Helping 15
Authoritative 3
Individualistic 2
422 TAKEUCHI
As Tab le 4 indicates, in both friend groups and teacher-assigned groups,
focal students tended to be positioned as novices. However, when working
with friends, these students also accessed the positional identity of experts,
meaning that there were occasions when ELLs offered their expertise in
relation to tasks. In non-friend groups, there were occasions when focal
students were positioned as subordinates, even when their peers did not
necessarily have a sufficient knowledge basis to merit a dominant role. In
these interactions, ELLs were forced to follow others because certain tasks
were taken away from them or because they were denied the opportunity to
participate.
Qualitative Characteristics in Friend Groups and Teacher-Assigned
Groups
In this section, I examine interactional characteristics when ELLs worked with
friends whom they selected versus with teacher-assigned peers. The following
excerpts of interactions were selected to show both the most frequently occurring
patterns of interactions observed in friend and teacher-assigned groups and the
patterns unique to each group.
Helping Work Practice, ELLs as Novices (Teacher-Assigned
Groups). The relationships constructed in the teacher-assigned groups
were characterized by ELLs staying in a position of being instructed,
helped, and given the correct answers. As the following episodes
demonstrate, one of the students (i.e., the student who was perceived to be
good at mathematics) played the role of a teacher, and the knowledge
presented by that student was not questioned by his or her peers. The
conversation did not yield opportunities for challenging, revising, and
exploring ideas. I describe this process in further detail by drawing from
the following episode of a teacher-assigned pair between Ajmal, who was a
newly arrived ELL, and his peer, Craig, who was considered to be good at
mathematics. Craig’s first language was English, whereas Ajmal’sfirst
language was Farsi.
In this episode, Ajmal and Craig were working on the following word
problem, which was written on the blackboard: “The archery team A hit 367
times. Team B hit 412 times. Did the two teams together hit 800 times? If not, by
how much did they miss?”They were given one sheet of chart paper between
them and were expected to provide one answer. Initially Craig alone read the
word problem aloud.
FRIENDSHIPS AND GROUP WORK 423
Excerpt 1 (November 19)
The interaction (e.g., utterances 8–10) in Excerpt 1 is characterized by the
initiation–response–evaluation pattern (Mehan, 1979). Craig provided Ajmal with
step-by-step instructions without engaging in discussions of what was being asked in
the problem or how to solve the problem (utterances 5, 8, and 11). Craig broke down
the addition of three-digit numbers (367 + 412) into several additions of single-digit
numbers (7 + 2, 6 + 1, 3 + 4). As observed in Craig’s approval of the answers
(utterances 10, 14) and in his answer to his own question (utterance 7), Craig was
checking whether Ajmal could answer his questions. Ajmal recorded the sum of
each digit by connecting two numbers with arrows but did not record the sum of the
whole numbers. Thus, the interaction did not reveal information about Ajmal’s
understanding of adding three-digit numbers, which was one of the learning goals
of this lesson. In this sense, this interaction is considered a simplification of a word
problem rather than an interaction leading to Ajmal’s engagement in solving word
problems. In the subsequent interaction, the teacher checked on the group and
worked with Ajmal to check his comprehension of the word problem. Because
Ajmal responded that he did not understand the problem, the teacher explained the
meaning of some words, such as archery, using gestures of drawing a bow.
1 00:00:06 Craig Four hundred twelve, okay?
Ajmal holds a pen. Craig and Ajmal both look at the chart paper.
2 00:00:10 Craig Four.
Ajmal writes. Craig watches what Ajmal is writing.
3 00:00:14 Craig Yeah.
Ajmal looks up and at Craig.
4 00:00:20 Craig Twelve.
Ajmal writes.
5 00:01:03 Craig Seven plus two?
6 00:01:06 Ajmal Seven plus two is.
Craig waits for Ajmal.
7 00:01:28 Craig Nine.
Craig writes on the chart paper.
8 00:01:43 Craig Okay, six plus one. What’s six plus one?
9 00:01:52 Ajmal Seven.
10 00:01:55 Craig Yes, seven.
This time, Craig writes down the number.
11 00:02:27 Craig Three plus four is?
He looks at Ajmal.
12 00:02:30 Ajmal Three plus four.
13 00:02:33 Ajmal Seven.
14 00:02:35 Craig Okay, write that down.
15 00:02:36 Ajmal Here?
16 00:02:41 Craig Yeah.
424 TAKEUCHI
In these interactions, Craig did not engage in a discussion about his current
mathematical understanding. For example, to add three-digit numbers, Craig invented
a system of notation that connected each place value with arrows (see Figure 1). This
notation can be difficult to transfer to addition with regrouping; however, this issue
was not addressed in the group. Instead, as demonstrated in Excerpt 1, Craig gave
instructions on how to write the answers, and Ajmal strictly followed his instructions.
Language learning opportunities in this interaction between Ajmal and Craig were
limited to spelling feedback, as observed in Excerpt 2. Craig gave an answer to the
word problem, and Ajmal copied it down. In this process, Craig also gave spelling
instructions to Ajmal. Although this instruction provided Ajmal with an opportunity to
learn the spelling of words, it also reinforced Ajmal’s linguistic deficiencies and
hindered his engagement in conversations about the mathematical problem.
The interaction between Craig and Ajmal leaned toward a calculation orienta-
tion, focusing on identifying and performing procedures without a careful exam-
ination of contexts (Thompson, Philipp, Thompson, & Boyd, 1994). Craig’s initial
FIGURE 1 Work by Craig and Ajmal.
Excerpt 2 (November 19)
1 00:09:07 Craig Okay, you write, you write. “The archery academy.”
Ajmal writes.
2 00:09:14 Craig T-H-E
Craig spells it out for Ajmal.
Craig stands up and goes to point to the word archery in the word
problem written on the blackboard.
3 00:09:26 Craig A-R-C-H-E-R-Y
Craig watches over Ajmal.
4 00:09:28 Craig Write a little bigger than that.
Ajmal continues writing, and Craig observes what Ajmal is writing.
FRIENDSHIPS AND GROUP WORK 425
incorrect answer (“the archery academy would need to hit the target 131 more
times”) was maintained until the teacher later noted the mistake.
Similar interactional patterns were observed in group work between Sabina,
who was a newly arrived ELL, and a teacher-assigned partner, Cathy, who was
considered to be good at mathematics. During group work, Cathy asked several
times for Sabina’s ideas; however, Sabina did not contribute verbally and simply
agreed with Cathy’s ideas. An example of this type of interaction is given in
Excerpt 3. In this interaction, Sabina and Cathy worked together to identify and
write characteristics of various three-dimensional objects. They attempted to
identify the characteristics of an octagonal prism in front of them. Cathy took
the lead in completing the task but occasionally solicited Sabina’s ideas.
Excerpt 3 (February 3)
As is evident in this interaction, even when Cathy solicited Sabina’sideas
(utterances 5, 7, and 9), Sabina did not offer any. Cathy continued providing
opportunities for Sabina to contribute her ideas, such as by stating that she
had forgotten the term to describe a three-dimensional octagon or soliciting
Sabina’s ideas. Sabina did not express when she needed help; therefore,
from this interaction, it is difficult to identify how Cathy offered to help
Sabina.
Helping Work Practice, ELLs as Novices (Friend Groups).Asthe
following interaction demonstrates, in contrast to the interaction with the
student who was adept at mathematics, Sabina tended to express her
1 00:00:10 Cathy Cathy counts how many corners the shape has.
It’s an octagon.
2 00:00:17 Cathy I’m not sure how to call a [three-dimensional] octagon. I forgot.
3 00:00:21 Cathy I forgot what it’s called.
4 00:00:33 Cathy That has six bridges, I think.
She starts to write that down. Sabina does not talk.
5 00:00:44 Cathy Anything else?
6 00:00:54 Cathy Sabina takes the shape and continues looking at it. Cathy, without
consulting Sabina, writes down the answer.
It has 10 faces.
7 00:00:58 Cathy Anything else?
8 00:00:56 Sabina Sabina nods.
Yeah.
9 00:01:00 Cathy What?
10 00:01:03 Sabina Sabina holds the shape and looks at it. Sabina then shakes her head.
426 TAKEUCHI
problems and share her ideas when working with her friend. In the following
friend group episode, which occurred during the same period as Excerpt 3,
Sabina was working with her friend Jasmine. Jasmine was an immigrant
student from Pakistan but was not receiving ESL instruction because she
hadbeeninCanadaformorethan2years.Whengiventheopportunityto
select their partners, Sabina and Jasmine chose to work with each other. They
wereeachprovidedwithaworksheet,andthetaskwastocalculatethearea
of each given shape. In this particular episode, they worked to calculate the
areaofarectangle(height=3cm,width=5cm).Incontrasttotheprevious
interactions with power asymmetry, the following interaction was
characterized by an equal power balance between the students, and Sabina
explicitly raised questions and told Jasmine when she needed help. In this
case, Sabina was unsure how to calculate the area of the rectangle. In the
following interaction in Excerpt 4, Sabina initiated a conversation by asking
“What’sabase?”Jasmine answered Sabina’s question by providing
information on how to compute the area, assuming that Sabina was asking
what the length of a base was. Even after this interaction, Sabina expressed
uncertainty about calculating the area. In the subsequent interaction, Jasmine
clarified the meanings of the base and the height of a rectangle.
Excerpt 4 (February 18)
1 00:15:05 Sabina What’s a base?
Jasmine shows her work to Sabina and begins explaining.
2 00:15:15 Jasmine There’s two over here, and this is three, so two over here and three over
here.
3 00:15:18 Jasmine See, three times two, so six units.
4 00:15:22 Sabina So, six?
5 00:15:26 Jasmine So, over here, one, two, three, it’s three.
6 00:15:29 Sabina No, no, no …we have to do this one first.
Jasmine moves on to the next question.
7 00:15:39 Jasmine Jasmine talks to herself.
Three times five …three, six, nine, twelve, fifteen.…
Jasmine writes.
8 00:15:47 Sabina What?
9 00:15:53 Jasmine Jasmine shows her work to Sabina.
See, over here, it’s three, and then, over here, it’s five, so, you do three
times five; how much is it?
10 00:15:56 Jasmine Jasmine answers her own question.
Three, six, nine, twelve, and fifteen! See? Get it?
Sabina also looks at the problem and starts writing while saying,
“Ohhhh.”
11 00:16:02 Sabina But how do you get three?
FRIENDSHIPS AND GROUP WORK 427
This example can be contrasted with interactions in a teacher-assigned
group. Although Sabina was still positioned as a novice and Jasmine as an
expert in this interaction, Sabina was able to clarify when she needed help
and what she did not understand. Sabina was often more talkative when
workingwithJasminethanwhensheworkedwithstudentswhowereper-
ceived as being good at mathematics.
Collaborative Work Practice, ELLs as Experts (Friend Group). Here I
present an example from episodes classified as collaborative work practices in
which Sabina was positioned as an expert. In this friend group interaction, Sabina
and Jasmine worked together on a textbook problem regarding appropriate units
for measuring various objects (such as desks, pencil cases, and students’heights).
Excerpt 5 (February 11)
1
Jasmine does not respond.
12 00:16:04 Sabina How do you get three?
13 00:16:06 Jasmine Jasmine points at her worksheet.
Over here.
14 00:16:08 Jasmine Jasmine points to the picture on the worksheet, and Sabina leans over
Jasmine’s desk and looks at it.
One, two, three, this is the height.
15 00:16:14 Jasmine Jasmine draws on the picture on the worksheet.
This is called base and this is called height.
16 00:16:16 Sabina Oh …now I get it.
1 00:15:39 Jasmine Jasmine reads aloud the word problem from the textbook (with only one
book between them).
Which unit would be best …perimeter of each object …explain your
choice.
Sabina is also looking at the textbook.
2 00:15:44 Jasmine Jasmine stops.
Ah?
3 00:15:58 Jasmine Ohhhh …so only what we do here, we’ll write a, b, c, d and what we
would choose and what we would choose for this one. Sabina points
to the textbook.
4 00:16:00 Jasmine I know. What we would choose, like …
5 00:16:02 Jasmine Jasmine picks up an object.
It stinks! Ew …
Sabina laughs.
6 00:16:15 Jasmine Jasmine returns to looking at the textbook.
428 TAKEUCHI
In both Excerpts 4 and 5, Sabina’s partner used questions to elicit Sabina’s
ideas (i.e., “What do you think?”“What unit would you use?”“Anything else?”).
This type of “other-monitoring”question (Goos, Galbraith, & Renshaw, 2002,p.
199) is a characteristic of collaborative group work. In Excerpt 5, Sabina decided
their final answer. In this process, Sabina was able to use her notebook as a
resource in which she had recorded the information given in class.
The interaction between friends in Excerpt 5 was characterized by reciprocity
in conversational turns. Utterances were divided equally; thus, there were more
opportunities for Sabina to participate. Their relationship was already well
established before they engaged in group work. This established relationship
contributed not only to the mutual participation of both students but also to a
focus on the content. When Jasmine went off task in conversation (in utterance
5), Sabina reacted by laughing with her; however, they quickly returned to
discussing the mathematical problem. Thus, their interaction tended to focus on
content rather than on off-task conversations. The next interaction shows how a
discussion of mathematical content can be sidetracked if the relationship between
group members is not well established.
Authoritative Work Practice, ELLs as Subordinates (Teacher-Assigned
Groups). Excerpt 6, taken from a teacher-assigned group, illustrates how content
space can be sidetracked when the relationship is not well established. Karim,
another newly arrived ELL, worked with Michael, who sat close to him. Their
work practice during group work was characterized as authoritative because Michael
unilaterally rejected Karim’s contributions. In the interaction in Excerpt 6, they were
solving a problem on elapsed time (how much time had elapsed between 7:40 a.m.
and 9:15 a.m.). Just before the interaction in Excerpt 6, the teacher had asked
1
For these things, what kind of unit would you use? Would you use
kilometers? Would you use millimeters?
7 00:16:14 Sabina Hmmm …Let’s use centimeters.
8 00:16:24 Jasmine No, but, okay, so, for teacher’s desks, what would you use?
9 00:16:22 Sabina Kilometers?
10 00:16:26 Sabina Millimeters?
11 00:16:38 Jasmine Hmmm …What did we use for our desks? Did we use millimeters?
12 00:16:38 Sabina Yeah.
13 00:16:41 Sabina Wait, let me …
Sabina flips through her notebook.
14 00:16:58 Sabina She turns to the page on which the information is written. Anyways …
we used for our desks centimeters.
15 00:17:18 Jasmine Jasmine mumbles “centimeters”and then starts to write this down in
her notebook.
FRIENDSHIPS AND GROUP WORK 429
Michael and Karim to discuss each other’s work because they had reached different
answers. They did not begin a discussion; instead, Michael continuously criticized
and mocked Karim’s handwriting (utterances 5–8). Even after the teacher checked
their work and asked them to discuss the differences between their answers, they still
did not begin discussing the problem (utterances 12–16) and instead played with
pencils. Their relationship was not collaborative, as observed in the utterance by
Michael mocking Karim’s pencil (utterances 14–16).
Excerpt 6 (March 11)
1 00:03:31 Michael Michael looks at Karim’s notebook with a yawn.
It’s not supposed to be one hour—but it’s supposed to be 35 minutes.
Karim leans over to Michael’s desk.
2 00:03:33 Karim Karim looks at his own notebook, which Michael is holding.
One hour.
3 00:03:38 Michael Michael also looks at Karim’s notebook and asks him.
…And how long is that one?
4 00:03:42 Karim Karim mumbles his answer [inaudible].
5 00:03:53 Michael Michael laughs out loud.
Yeah. You didn’t write one full hour. You wrote 43 hours and 15
minutes.
6 00:03:56 Michael 43 hours and 15.
7 00:04:01 Karim Karim yells.
That one is for this.
8 00:04:03 Michael Yeah, but that can’t be 43 hours.
9 00:04:04 Michael I get this.
10 00:04:09 Karim This one?
11 00:04:14 Michael Michael, while erasing what Karim wrote, says the following:
How can that be 43 hours?
Michael continues to make fun of Karim’s handwriting. As they become
noisy, the teacher checks in on the group.
12 00:04:51 Teacher The teacher looks at both of their work and compares their answers.
So, this answer says “35 minutes,”and you have a very different
answer here. You have four hours …No, one hour and 35 minutes.
You guys should check this one.
The teacher leaves.
13 00:05:32 Teacher As Michael and Karim are playing with pencils and erasers, the teacher
returns.
Why do you have a different answer here?
She then leaves.
14 00:06:04 Michael When the teacher leaves, Karim and Michael start to play with pencils
again.
Is that yours? Where did you get it?
15 00:06:08 Karim At Dollarama.
16 00:06:10 Michael Michael laughs.
Huh, Dollarama.
430 TAKEUCHI
The authoritative relationship between Karim and Michael affected how they
discussed the problem. As seen in utterance 12 in Excerpt 6, the teacher noted the
difference between Karim’s answer (1 hr and 35 min) and Michael’s answer (35
min). For this particular problem, Karim’s answer was correct (as seen in
utterances 1 and 12). Noticing this difference, the teacher encouraged the stu-
dents to discuss their answers on their own. However, when the teacher was not
monitoring their work, Michael and Karim did not begin a discussion; instead,
Michael teased Karim about his handwriting or his belongings.
Throughout this interaction, Karim was not positioned as a competent contribu-
tor; therefore, his ideas were not even solicited. Even though Karim’sanswerwas
correct, Michael insisted that his answer was correct throughout (utterances 1 and 9)
and did not listen to Karim, even after the teacher intervened and encouraged
discussion. In this case, Michael’s authority was backed by his social authority
rather than his mathematical authority. This example shows how a relational space
can interfere with a content space that is being constructed. In the data set analyzed
for this article, this type of authoritative work practice was observed only in teacher-
assigned groups, in which friendships were not well established.
DISCUSSION
This ethnographic study examined students’opportunities to learn in linguisti-
cally diverse mathematics classrooms in a Canadian elementary school, given the
contextual change of group work. I examined how newly arrived ELLs’oppor-
tunities to learn differ between student-selected friend groups and teacher-
assigned groups. Based on analyses of video-recorded interactions, this study
revealed that ELLs tended to gain access to a wider variety of work practices and
positional identities when working with friends. The interactions in friend groups
demonstrated that ELLs were able to express their difficulties and problems to
their peers. In friend groups, ELLs were also positioned as experts and engaged
in collaborative work practices in which ELLs were able to further engage in
discussion and offer ideas.
Relatively few studies have examined linguistic diversity in relation to group
work processes in mathematics classrooms. Issues examined by previous studies
include how social organization and pedagogical orientations impact students’
mathematical communication in groups (Brenner, 1998) and how bilingual
learners’languages served as resources for social and problem-solving functions
during group work in mathematics classrooms (Moschkovich, 2007; Zahner &
Moschkovich, 2011). Little investigation has been conducted on the relationship
between friendship and group work in linguistically diverse content classrooms.
Newly arrived ELLs tend to be transient and are thus more vulnerable to
challenges in establishing friendships, partially as a result of this mobility
FRIENDSHIPS AND GROUP WORK 431
(Gunderson, D’Silva, & Odo, 2012). In addition, in racially and linguistically
heterogeneous schools, friendships and social groupings can be based on racial
and linguistic groups (Olson, 1997) and friendship formation can influence how
students experience group work. Consequently, this study contributes to the
discussion on learning through group work by revealing the role of friendship
for mathematics learning in the context of various groups in linguistically and
racially heterogeneous classrooms.
Opportunities to Learn and Identities in Group Work
The findings from this study can be partially explained by some of the positive
interactional characteristics among friends: understanding each other better, hav-
ing a stronger commitment to maintaining a good relationship, and feeling more
secure in working with each other (Azmitia & Montgomery, 1993; Fonzi et al.,
1997; Hanham & McCormick, 2009; Strough et al., 2001; Zajac & Hartup,
1997). However, this ethnographic study does not aim to demonstrate a causal
relationship between friendship and ELLs’opportunities to learn in group work.
Rather, this study highlights how opportunities to learn are contextualized by
students’multiple layers of identities and their friendships constructed inside and
outside classrooms. In this light, it is noteworthy that the teacher initially
assumed that the best group members for newly arrived ELLs would be students
who were categorized as “being mathematically adept,”“exhibiting leadership,”
and “caring.”The interactions presented in teacher-assigned groups show that
students who were assumed to be mathematically competent tended to offer more
ideas, assume the lead, and have more opportunities to discuss ideas. In contrast,
newly arrived ELLs tended to assume a more passive role and occasionally
depended on peers to solve problems. This finding can be interpreted from
positioning theory, which maintains that a person who is positioned as incompe-
tent in a certain field will not contribute to discussions in that field (Harré & Van
Lagenhove, 1999). Given that previous studies have maintained that students
who engage in explanations and participate in elaborate discussions tend to
benefit more from group work (Chizhik, 2001; Webb, 1985), this difference in
participation can further perpetuate the existing learning gap between ELLs and
students who are considered to be adept at mathematics.
By focusing on friendship as a context of group work, the current research
advances the discussion on social identities and power dynamics that influence
student collaboration (Engle, Langer-Osuna, & McKinney de Royston, 2014;
Esmonde & Langer-Osuna, 2013; Langer-Osuna, 2011). Rather than treating
power dynamics as fixed, this study compared and contrasted ELLs’opportu-
nities to learn under different contexts of group work. Furthermore, this study
provides insight into students’friendship formation. When given a choice,
students did not select teacher-assigned partners for group work but rather
432 TAKEUCHI
chose students with whom they played during recess. This finding supports the
idea that students’friendship formation and group member preferences can be
influenced by implicit power dynamics shaped through students’social identities
(e.g., race, and gender; Esmonde et al., 2009). Further analysis of this aspect will
be beneficial to consider whether and how the group work process can challenge
existing group and friendship formation and power relations in linguistically
diverse classrooms (Cooper & Slavin, 2001).
This study also contributes to the discussion on the unity of affective and
intellectual processes. By critiquing the dominance of cognition in psychological
research on learning, Holzman (2009) maintained that cognition and emotion are
unified processes of learning and development; therefore, the zone of proximal
development proposed by Vygotsky (1978) can be interpreted as the zone of
emotional development. Because group work is a collective space in which indivi-
duals learn and develop together, the way they feel about working together cannot be
less significant than the way they solve a task or what they collectively think.
Limitations
The findings presented here are based on an ethnographic study in a single
school. To further investigate the complex relationship between friendship and
group work involving ELLs, additional studies with various methodologies will
be necessary. For example, this study did not measure students’mathematical
and linguistic performance subsequent to group work. As shown by Barron
(2003), such an investigation can yield rich findings on whether and how
group work interactions can be internalized by each member of a group. In this
study, I did not combine insights gained from group work learning or other
contexts of learning such as whole-class discussions, because the main purpose
of this study was to investigate different contexts of group work. In future
research, a cross-analysis across group work, individual performance, and
whole-class discussions can be meaningful to identify the relationships between
different contexts of learning.
In addition, because this ethnographic study compared interactions in teacher-
assigned groups (which were mainly observed earlier in the year) and friend
groups (which occurred later in the year), there is a potential order effect in the
results I presented. I partially addressed this limitation by including and analyz-
ing the interactions in both types of groups occurring in the same month. Given
that academic language development for ELLs generally takes 5 years or longer
(Cummins, 2000), the potential order effect can be assumed to play a minimal
role for the difference in ELLs’linguistic performance between the two types of
groups over the academic year. Further trajectory analysis beyond an academic
year will be meaningful to help reveal ELLs’mathematics language development
in group work over a longer period of time.
FRIENDSHIPS AND GROUP WORK 433
Pedagogical Implications
This study aims to initiate discussion regarding how and when ELLs and/or
linguistic minority students can meaningfully engage in group work and ulti-
mately enhance their learning opportunities. In the classroom examined in this
study, the teacher regularly observed which groupings were effective and how
students engaged in the interactions. The teacher keenly observed the students’
group work, and her observations led to flexibility in grouping the students. This
study highlights the significance of this type of experimentation by the teacher
for enhancing students’opportunities to learn during group work. This finding
corroborates previous research examining the role of teachers’discourse in
creating productive learning environments in linguistically diverse mathematics
classrooms (Aguirre & del Rosario Zavala, 2013; Takeuchi & Esmonde, 2011).
As noted by Barron (2003), learners simultaneously engage in a content space
and a relational space in group work. In group work, students not only discuss
the content or tasks but also engage in relationship building. As a significant part
of school life, friendships can affect students’classroom learning and identities in
school. In a group that adopts authoritative work practices, the inferior position
assigned to ELLs can be further reinforced. Because learning involves the
development of participant identities in communities of practice, it is important
to design cooperative group work that helps all students develop identities as
significant and competent contributors to a classroom community.
ACKNOWLEDGMENTS
I would like to thank Dr. Indigo Esmonde, Dr. Lesley Dookie, the editors, and the
anonymous reviewers for their careful reading and helpful comments on earlier
versions of this article. I also appreciate Dr. Hua Shen for her analytical input. I
would like to express my sincere appreciation to the teacher and the students who
welcomed me in their classrooms. A portion of these findings was presented at the
annual conference of the American Educational Research Association in 2013.
FUNDING
This work was supported in part by the Japan Society for the Promotion of
Science under Grants-in-Aid for Scientific Research (12J02927). Any opinions,
findings, and conclusions expressed herein are my own and do not necessarily
reflect the views of the funding agency.
434 TAKEUCHI
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