Running head: DEVELOPING AGENCY WITHIN THE MIDDLE-SCHOOL MATHEMATICS CLASSROOM 1
Developing Agency within the Middle-School Mathematics Classroom:
Authenticating the Interrelationship between Mathematical and Social Identity
Stephen Santana
Vanderbilt University
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Abstract
In the traditional middle school mathematics classroom, learning is viewed as a
passive process in which students receive knowledge via the didactic instruction of
the teacher. Learning is a social process, however, and adolescence is a development
period in which social interactions become more salient in students’ formation of
identity. The current norms that pervade the middle school mathematics classroom
must be transformed to allow for new conceptions of epistemic authority.
Classrooms must become communities of learning in which students share the
power to construct and negotiate knowledge. In this paper, I focus on the
interrelationship of adolescent social development and mathematical agency and
how the mathematics classroom should be structured with an understanding of
students’ social development. I assert that without a positive interdependence
between students, mathematical agency will be hindered and all members of the
learning community will be negatively affected.
Keywords: social development, agency, community, sociomathematic
norms, care
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Current mathematics education literature is heavily informed by research
within the domain of cognitive development with the expectation that the
knowledge of how, what, and when students learn will ultimately help to shape
mathematics curriculum, pedagogy, and classrooms environments. More
specifically, there has been a call to shift from traditional didactic instruction of
mathematics to a more connected approach, straying from rote memorization and
procedural mathematical practices (Boaler & Greeno, 2000). By the last decade of
the twentieth century, theories about situated learning began to emerge more than
ever, claiming that “…behaviors and practices of students in mathematical situations
are not solely mathematical, nor individual, but are emergent as part of the
relationships formed between learners and the people and systems of their
environments” (Boaler, 1999, p. 261). This shift from individual to collective
learning has been adopted and endorsed by experts in the field of mathematics, but
rarely has it been explicitly linked to one of its most salient components: social
development of the early adolescent.
While the research on cultivating classroom communities or communities of
learners does support the social nature of learning, there is often no direct link
between its social components, research within the domain of social development,
and research within domain-specific fields. In this paper, I will focus on how to build
community in the middle school mathematics classroom tailored to adolescent
social development that facilitates students’ mathematic success while
simultaneously fostering their positive social development. My goal is to synthesize
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the research on adolescent social development with research about communitybased mathematics learning environments in such a way that classroom practices
are informed by how students develop socially, authenticating the interrelationship
between their mathematical and social identities.
I will define mathematical success as students’ positive mathematical
identity through their development of mathematical agency, which will be fostered
in a classroom community grounded in sociomathematical norms that hold all
students accountable for the construction of mathematical knowledge (Boaler &
Humphreys, 2005). The following practices informed by adolescent social
development will be explored in order to shape these sociomathematical norms that
will promote student success: (1) reducing social comparison; (2) creating a
mastery-oriented classroom, as opposed to the performance-oriented environment
typically encountered in middle schools; and (3) engendering prosocial behavior
between students. I focus on these three areas of social development primarily due
to their salient presence specifically during adolescent development and secondly
due to the notable clash between the configuration of the middle school experience
and the social development of early adolescents.
The Mismatch between the Adolescent and the Middle School
Before delving any further, I must define the school context in which early
adolescents participate. Middle schools typically span grades 6–8 or 5–8, which
cover the pivotal years of early adolescence (Rockoff & Lockwood, 2010, p. 1051).
The transition between elementary school and middle school can be a difficult time
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for students, especially due to a mismatch at the middle-school level between
“educational practices…[and] the adolescent’s needs” (Harter, 2008, p. 238). In
addition, Eccles and Roeser (2011) insist that the widespread decline in motivation
and achievement in the transition from elementary to middle school reflects
developmentally inappropriate changes in the nature of schooling (p. 236).
Throughout this paper, I seek provide alternatives to these norms that seek to
optimize the system that is already in place in order to create a middle school
environment that is sensitive to the needs of early adolescents and that mitigates
the potential liabilities that may ensue from such a transition.
Mathematics Education as a Social Practice
Mathematics classrooms have by and large been characterized as teachercentered environments in which instruction consists of direct explanation and
where students work independently at their seats (Brown, Stein, & Forman, 1996, p.
63). Boaler (2002) juxtaposes this very kind of conventional mathematics classroom
environment with that of a school environment that promotes a progressive
approach to mathematics education, emphasizing the importance between
knowledge and practice. The notion of learning as a social process is far from novel;
rather, John Dewey (1897), the father of the Progressive movement in American
education, brought it to the forefront of educational theory:
The school is primarily a social institution. Education being a social process,
the school is simply that form of community life in which all those agencies
are concentrated that will be most effective in bringing the child to share in
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the inherited resources of the race, and to use his own powers for social
ends. (p. 430)
Myriad educational practitioners and theorists throughout the twentieth and
twenty-first centuries have supported Dewey’s pedagogic creed, validated through
Vgotsky’s (1978) research and continuing to that of Bransford, Brown, and Cocking
(2000). The Russian psychologist, Lev Vygotsky, affirms in his 1978 work Mind in
Society, “Human learning presupposes a specific social nature and a process by
which children grow into the intellectual life of those around them” (p. 88). For
these reasons, the social nature of learning should not and cannot be divorced from
the practice of mathematics. The mathematics classroom should be a figured world
in which students can construct their social and mathematical identities through
social practice (Boaler & Greeno, 2000, p. 173).
The Crossroads of Learning and Development
Drawing from the knowledge that learning is a social process, it is necessary
to understand how social development and learning correlate. Bransford et al.
(2000) argue, “Development and learning are not two parallel processes. . . .
Learning is promoted and regulated both by children’s biology and ecology, and
learning produces development” (pp. 112-113). The movement to define and
implement developmentally appropriate best-practices within education has
sparked the authorization of developmental research in shaping curriculum and the
classroom environment; however, if learning is simultaneously a social process and
a medium of development, then I contend that research and practices pertaining to
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learning mathematics and the social development of students should be mutually
informed. Early adolescence is a critical transitional period during which students
become more independent and begin to redefine interdependence with peers
(Collins & Steinberg, 2008). Due to the gravity of this developmental period, schools,
classrooms, and curricula must be organized in such a way that recognizes and
supports students during their early adolescent years. In this way, the means by
which students learn mathematics should support the development of their social
identities while concurrently capitalizing upon students’ social development in
order to promote mathematical success. Ann Brown (1997) succinctly asserts, “…a
knowledge of developmental psychology is not just nice but necessary if one want to
study learning in children, in whatever setting one chooses” (p. 400). This raises
another point: it is also necessary to make a third connection between social
development, students’ learning, and their learning environment. The next section
provides this link by defining students’ learning environments in terms of their peer
interactions.
Cultivating a Community of Learning
Communities of practice, as coined by Wenger, McDermott, and Snyder
(2002), are everywhere, present in “every aspect of human life” (p. 5). The authors
explain, “Communities of practice are groups of people who share a concern, a set of
problems, or a passion about a topic, and who deepen their knowledge and
expertise in this area by interacting on an ongoing basis” (ibid, p. 4). Using this
definition, schools, and on a micro level, classrooms, can be communities of practice
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but often lack the interaction piece that is necessary of such a community. When
“classroom practices…emphasize the reproduction of predetermined methods and
procedures,” students are positioned in a way that learning becomes passive and
unconnected to others in the classroom (Gresalfi & Cobb, 2006, pp. 50-51). In order
to foster interaction in the classroom and create a community of learners, there
must be a guiding set of learning principles in place within the classroom that
counteract what Boaler and Greeno (2000) call received, subjective, and separate
knowing, therefore supporting connected knowing through the construction of
knowledge by means of interaction with others (p. 174).
I draw my definition of a community of learners from Ann Brown’s (1997)
research on her Fostering Communities of Learners (FCL) program. She states, “The
FCL community relies on the development of a discourse genre in which
constructive discussion, questioning, querying, and criticism are the mode rather
than the exception” (p. 406). Communication is fundamental in a community of
learners, but it must be situated in an environment that endorses social learning.
Borrowed from Jerry Bruner (1996), Brown offers four principles of learning that
she claims are salient to the formation of a positive learning community: agency,
reflection, collaboration, culture (i.e., of learning, negotiating, sharing, and
producing) (pp. 411-412). In a community of learners, these four principles should
be inextricably linked in order to maintain a positive learning atmosphere.
With these principles in mind, Brown also seeks to reform the conception of
curriculum. While she places high esteem upon deep disciplinary content, she
argues that in a true community of learners, students are partially responsible for
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creating their own curriculum (ibid, p. 407). This allows a certain autonomy in
students’ learning, but it does not sacrifice high standards of understanding. In their
pursuit to broaden the narrow conceptions of mathematics curriculum, the National
Council of Teachers of Mathematics (NCTM) (2000) explains that an effective
mathematics curriculum goes beyond a collection of activities. NCTM proposes that
mathematical ideas must be connected and should be used to construct a coherent
understanding of concepts that build upon each other. Inviting students to
participate in a community of learners in which they are expected to construct
curriculum and knowledge communally will allow students to become actively
engaged in their learning, engendering intrinsic motivation to learn and potentially
minimizing future academic failure or even dropping out of school. (Johnson.
Johnson, & Roseth, 2010, p. 4). The role of the students in shaping the curriculum
reveals an even greater need for students to be confident mathematical agents.
Mathematical Agency Fostered by a Community of Learners
Adapting Pickering’s (1995) work on scientific agency, Gresalfi and Cobb
(2006) bifurcately define the concept of mathematical agency. Disciplinary agency
involves applying a mathematical method to solve a problem, whereas conceptual
agency includes “choosing methods and developing meanings and relations between
concepts and principles” (p. 52). In other words, conceptual agency can be
understood as the ability to know what mathematical tool to use, when to use it, and
why. As I discuss agency, I wish to focus on conceptual agency as the goal for
mathematic success, as it deviates from the procedural norms of many mathematics
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classrooms and drives students to become active learners within their learning
communities (Boaler & Greeno, 2000). As Fosnot and Dolk (2002) indicate,
“Children who learn how to think, rather than to apply the same procedures by rote
regardless of the numbers, will be empowered” (p. 106).
Agency as Individual Power
In many mathematics classrooms teachers become the proprietor of
epistemic authority, authoring a didactical contract in which the teacher has the
power to create and disseminate knowledge while the students passively receive it
(Herbst, 2004, p. 11). This contract prevents students from developing their own
mathematical agency, leaving them powerless in the construction of mathematical
knowledge. According to Deci and Ryan’s (2002) self-determination theory as cited
by Wigfield, Eccles, Roeser, and Schiefele (2008), humans have the psychological
need for autonomy: “When individuals’ behavior is self-determined, they are
psychologically healthier and tend to be intrinsically motivated” (p. 410).
Adolescence is marked by the desire to acquire autonomy—to be as Kuhn and
Franklin (2008) maintain, “producers of their own development” (p. 543). With this
in mind, the mathematics classroom environment must be structured in a way that
allows individuals to share power without surrendering their personal agency as
learners (Boaler & Greeno, 2000).
Cornelius and Herrenkohl (2004) analyze the dynamic of power in
classrooms and assert that it involves three conceptualizations: ownership of ideas,
partisanship, and persuasive discourse. Focusing first on the ownership of ideas, it is
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important to connect students’ power to take ownership of ideas and their role as
mathematical agents. When given the opportunity to take ownership of his or her
ideas, “the student perceives a higher degree of flexibility in using it, in asking
questions of it, and sometimes…in dismissing it when it fails to explain observable
phenomena” (ibid, p. 481). In essence, it allows students to select their own
mathematical tools, apply them when and where they are needed, and reflect upon
their conceptual implications.
Agency as Collective Power
Once students have individual power as mathematical agents, students are
then able form power relationships with other members of the learning community.
Partisanship, Cornelius and Herrenkohl’s (2004) second conceptualization of power,
“describes relationships of power among students that can develop through their
interactions with concepts and with each other” (p. 470). These relationships of
power can be used both constructively and destructively if not fostered within a
solid community of learners. On the one hand, they can serve to empower all
students regardless of race, gender, or mathematical understanding (ibid). However,
individual agency, if not cultivated socially, can be used to oppress and/or invalidate
the ideas of other mathematical agents in the classroom, possibly resulting in a
negative perception in a student’s personal and/or mathematical identity. According
to Harter (2008), “Classmate support in the form of approval represents more
seemingly objective feedback about one’s competencies, adequacy, and worth as a
person” (p. 233). Partisanship, thus, should be viewed as a means for mathematical
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agents to contribute to the social construction of knowledge, allowing all students
within the learning community to take ownership of the ideas shared in the
classroom. As Goos (2004) explains, “Working in collaborative peer groups,
students have an opportunity to own the ideas they are constructing and to
experience themselves and their partners as active participants in creating personal
mathematical insights” (p. 263).
Shaping Sociomathematic Norms
As previously noted, learning is a social process that requires what Johnson
et al. (2010) call a positive interdependence between members of the learning
community (p. 3). Students are able to reach their mathematical goals “if and only if
the other individuals with whom they are cooperatively linked also reach their
goals. Participants, therefore, promote each other’s efforts to achieve the goals”
(ibid). This positive interdependence pushes students to empower others in order
to promote collective success. Cultivating a classroom environment that supports
this type of interdependence requires a shared recognition and agreement that
mathematic work is a “collective enterprise” (Boaler & Humphreys, 2005, p. 51). I
contend that this agreement can be achieved through the establishment of what
Boaler and Humphreys (2005)1 term sociomathematic norms in the classroom.
These norms move beyond mere communication of mathematical ideas; they
embody “a concern for mutual understanding” in that students “are actively working
1
Adapted from Schwartz, D. 1999. The productive agency that drives collaborative learning. In P.
Dillenbourg (Ed.), Collaborative learning: Cognitive and computational approaches (p. 197-241). New
York, NY: Pergamon.
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to help others understand” (ibid, p. 116). In doing so, students demonstrate their
agency by providing evidence for their thinking through Cornelius and Herrenkohl’s
(2004) third conceptualization of power, persuasive discourse. The authors contend
that the sociomathematical norm of justification to support claims serves as a check
and balance of power in the classroom and serves as a metacognitive tool to check
for personal understanding (p. 488).
Sociomathematic norms also provide consistent expectations within the
mathematics classroom without compromising mathematic flexibility or rigor.
While it may be easier to uphold high expectations for students with stronger
executive functions and high academic achievement, Blair and Diamond (2008)
warn against expecting lesser quality work and poor self-control from students with
weaker executive functions and lower academic achievement. Lowered
expectations can cause students to hold negative self-perceptions, thus perpetuating
poor achievement. In light of this self-fulfilling prophecy, Blair and Diamond
contend:
The trajectories of children who start with better self-regulation and
executive functions, and worse, would be expected to diverge more and more
each year as the positive feedback loop for the former, and the negative
feedback loop for the latter, progressively enlarge what might be relatively
small differences at the outset, producing an achievement gap that widens
each year. (pp. 905-906)
Establishing strong sociomathematical norms within the classroom community will
allow for students at all levels of achievement to participate in the construction of
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mathematical understanding and will offer them epistemic power within their
classrooms.
Unfortunately, common social norms such as negative interdependence or
even no interdependence between students are ever-present in middle school
classrooms (Johnson et al., 2010). In the following sections, I target three widely
researched areas of adolescent social development that I believe require special
attention in relation to engendering sociomathematical norms within a community
of learners in the middle school mathematics classroom that supports mathematical
agency. These developmental areas have not been chosen arbitrarily; rather, I argue
that without lending adequate attention to their explicit connection to cultivating
positive social norms within the learning community, it will be impossible to foster
positive and consistent sociomathematical norms in the classroom, thus diminishing
the opportunities for individual mathematical agency.
Redefining Middle School Classroom Norms
Norms of social comparison, performance-oriented dispositions, and
antisocial student behavior pervade the middle school environment, and teachers
must acknowledge their existence and work to counteract their negative effects in
both students’ social and mathematical identities. Blakemore and Frith (2005)
maintain, “The teacher’s values, beliefs and attitude to learning could be as
important in the learning process as the material being taught” (p. 463). Middle
school mathematics teachers thus have an important role to play in the classroom.
Beyond a deep understanding of pedagogy and content knowledge, they must also
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employ an understanding of his or her students’ development in order to uphold
positive values and beliefs about student learning that will inherently influence the
classroom climate.
Lessening Social Comparison
The current middle school structure emphasizes student comparison, both
by teachers and by students. As cited by Harter (2008), Eccles and Midgley (1989)
contend that in the middle grades, “…there is considerably more emphasis on social
comparison (e.g., public posting of grades, ability grouping, or teachers, in their
feedback to classes, verbally acknowledging the personal results of competitive
activities)” (p. 238). These comparative practices can prove to be very harmful to a
students’ sense of self, negatively affecting academic achievement and self-esteem.
Also due to the “shift from effort to ability” in the transition from elementary to
middle school, students begin to attribute poor academic achievement with a lack of
intelligence, which is “…exacerbated in contexts of high public feedback and great
social comparison” (ibid). Middle school mathematics teachers must be aware of
the dangers of social comparison and must help to create a learning environment in
which students’ mathematical identities are supported and respected. Early
adolescence is already a period typified by a “heightened concern with how others
view the self,” and the classroom community cannot be structured in a way that
intensifies this apprehension (ibid, p. 237).
Moreover, competition in the classroom undermines the collaborative
process of social learning that middle school math teachers should seek to cultivate.
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Eccles and Roeser (2011) confirm this assertion through their review of Roseth,
Johnson, and Johnson’s (2008) meta-analysis of over 17,000 adolescents and the
effects of competitive, cooperative, or individualistic goal structures on the
achievement and peer relationships. The researchers “found that higher
achievement and more positive peer relationships were associated with cooperative
rather than competitive or individualistic goal structures” (p. 228). Ball (1991)
makes the case that it is important for teachers to be vigilant and pay attention to
students’ discourse in order to catch and correct the “long-established school norm”
of competitiveness in the mathematics classroom (p. 44). Teachers must also be
aware of the link between social comparison and performance-oriented instruction
and assessment. Ryan and Patrick (2011) affirm, “The promotion of performance
goals concerns an emphasis on competition and relative ability comparisons among
students in the classroom” (p. 442). For this reason, teachers must employ masteryoriented instruction and assessment in a learning environment dedicated to positive
mathematical and social identity.
Mastery-Oriented Instruction and Assessment
When students enter middle school, they are confronted with a culture that
values performance over mastery. As cited by Wigfield et al. (2008), Midgley (2002)
reveals the following dissonance between the elementary and middle school
environments:
(1) Elementary school teachers focus on mastery-oriented goals to a greater
extent than do middle school teachers, and (2) middle school students
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perceive school as more performance oriented than do elementary school
students. Thus, any observe changes in children’s goal orientations seem
very bound up in changes in the school goal culture. (p. 417)
The middle school curriculum should not be structured around drilling for top-tier
performance; rather, it should allow for discovery learning and cognitive conflict.
Van de Walle, Karp, & Bay-Williams (2010) clarify that while drill can be useful for
increasing efficiency with mathematical procedures or as review, it does not
promote mastery or understanding of concepts and perpetuates a procedural view
of mathematics (p. 69). In addition, the current middle school norms solely focused
on performance can be devastating to low-achieving students’ efficacy (Harter,
2008). A middle school curriculum that employs a mastery-oriented structure will
engage learners more effectively, as Wigfield et al. (2008) indicate in their research:
“…mastery-oriented children are more highly engaged in learning, use deeper
cognitive strategies, and are intrinsically motivated to learn” (p. 412).
One way in which teachers can move toward a norm of a mastery-oriented
classroom is by using praise cautiously (Van de Walle et al., 2010, p. 54). Instead of
praising correct answers, teachers might focus praise on effort and risk taking (p.
47) or provide “comments of interest and extension” (p. 54). These practices align
well with notion that all students’ thinking is valuable and that epistemic authority
does not solely belong to the teacher (cf. Dewey, 1910). Also, if teachers exclusively
focus on correct answers, students will become increasingly worried about making
errors (Bransford et al., 2000, pg. 61). Brown (1997) indicates the potential for
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learning that can be found in what she calls “fruitful errors” (p. 411). Fruitful errors
provide a springboard for learning and reflection. Lampert (2001) explains:
One of the hardest things to do in front of a group of one’s peers is to make a
mistake and admit one has made it, and correct it. Yet such a series of actions
is an essential component of academic character. (p. 266)
Although this is a difficult norm to overcome in the middle school mathematics
classroom, it is vital that students agree to allow mistakes in classroom as a
sociomathematical norm of the learning community. They should be viewed as
opportunities to reflect and examine errors in such a way that is productive in the
construction of mathematical knowledge and justification (Boaler & Humphreys,
2005).
A performance-oriented classroom, moreover, will most likely offer limited
opportunity for valid formative assessment. According to Bransford et al. (2000),
formative assessments are “ongoing assessments designed to make students’
thinking visible to both teachers and students” (p. 24). Correct answers do not
reveal student thinking (Van de Walle et al., 2010), thus leaving the teacher and
learning community unaware of individual thinking processes and inhibiting
students’ abilities to reflect metacognitively about their strategies. This reduces
students understanding of procedures as instrumental rather than relational,
forcing them to relinquish their mathematical agency (Boaler & Humphreys, 2005,
p. 9). The NCTM (2000) principles and standards also stress that assessment should
enhance learning and should be used as a valuable tool for learning, which cannot be
possible in a performance-oriented classroom. If the norm of mastery-oriented
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learning is nurtured in the middle school mathematics classroom, students will be
able to assess themselves and one other continuously in such a way that enhances
learning and conceptual agency for members of the community of learners.
Mitigating Antisocial Behavior
Antisocial behavior in adolescents can also be a deterrent in creating and
maintaining a positive community of learners in the middle school classroom. These
negative behaviors can be manifested through aggression, violence, bullying,
disrespect, and/or general distrust of peers and the teacher resulting in social
isolation (Dodge, Coie, & Lynam, 2008). Unfortunately, many intervention practices
have proven to perpetuate antisocial behaviors by grouping adolescents who
demonstrate these deviant behaviors, allowing them to negatively influence one
another (ibid, p. 452). While the school alone cannot regulate all antisocial behavior,
teachers can provide support for adolescents who demonstrate such behavior.
Marin and Brown (2008) prescribe a system of support that I believe can be
fostered by a solid community of learners:
The support of peers and teachers at school can have important
consequences for student well-being. Adolescents who feel that there are
people who care about them at school and feel connected to the school are
more likely to be academically motivated and less likely to engage in a
variety of negative behaviors…. (p. 6)
A community of learners that relies on a positive interdependence between peers
can help to regulate some negative behavior in the classroom. The general
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classroom environment can also play a role in regulating antisocial behavior. All
students will benefit from a nurturing and mutually supportive environment, but
Dodge et al. (2008) mark the even greater importance of such an environment for
students at risk for antisocial behavior.
Consistency is also key in minimizing antisocial behavior in the classroom.
Harter (2008) states, “Contradictory standards and feedback can also contribute to
a lowering of global self-esteem between early and middle adolescence” (p. 244).
For this reason, explicit and commonly understood sociomathematic norms are a
vital component of the community of learners. If norms such as justification of
mathematical thinking are not set by the community of learners, students will hold
on to their prior school norms. Ryan and Patrick (2001) support the
sociomathematical norm of mathematical discourse, explaining that “…legitimizing
opportunities for students to talk with one another and meet social needs may be
associated with decreased disruptive behavior in the classroom” (p. 441).
Additionally, Matsumara, Slater, and Crosson (2008) further support consistency for
prosocial expectations by stating, “Clear and explicit rules for prosocial, respectful
behavior [are] an important factor in fostering student participation in class
discussions” (p. 310). These prosocial classroom norms encourage discourse, which
consequently supports mathematical agency, revealing a cyclical relationship
between the ability to positively contribute to the community of learners and the
ability to establish mathematical agency as a member of said community.
Lastly, reflecting on Marin and Brown’s (2008) recommendations, the notion
of care seems to permeate the literature on fostering prosocial behavior as well as
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engendering positive classroom communities. In her book, The Challenge to Care in
Schools, Nel Noddings (1992) says that caring can have a transformative effect on
schools as long as both the carer and the cared-for form a reciprocal relationship in
which both parties offer and accept care. If a student does not accept care from a
peer or from the teacher, Noddings would argue that caring consequently does not
take place. Students must believe that the teacher and their peers can offer care in
order for them to accept it. Students demonstrating antisocial behavior may not feel
cared for under the common middle school norms, and Noddings makes clear that
“[t]he capacity to care may be dependent on adequate experience in being cared for”
(p. 22). Caring for students includes caring for their progress and learning (Ball &
Bass, 2003, p. 30). This can be achieved through the construction of a community of
learners in the mathematics classroom due to the fact that “relationships are
enhanced when children are truly learning, and learning is enhanced when children
are in a caring environment” (Matsumara et al., 2008, p. 295).
Conclusion
I have discussed how understanding adolescents’ social development is vital
in fostering a community of learners within the middle school mathematics
classroom. Without the formation of a solid community of learners, mathematical
power through individual and communal agency will be threatened, resulting in a
weakened understanding of mathematical concepts. The norms set by the
traditional classroom must be reformed to fit the needs of the learning community,
substituting socially and mathematically inhibiting norms for positive
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sociomathematical norms that create clear expectations for students. As Yackel,
Cobb, Wood, Wheatley, & Merkel (1990) suggest, the teacher and students must
establish a classroom norm that stipulates helping one’s peers to learn as a central
element of the students’ roles in within the learning community (p. 20).
Mathematical success is defined as personal conceptual agency, but it also entails
the mathematical agency of the whole community. In order for all students to be
successful mathematical agents, their dispositions and personal identities must be
positively related to the community of learners that constructs and defines
mathematical knowledge and understanding. Students must see themselves as
active and connected knowers and as accepted members of their peer group. Once
they are able to reconcile their mathematical and social identities, middle school
students will be better equipped to construct knowledge and to form positive social
relationships within the mathematics classroom that will support connected and
social learning.
DEVELOPING AGENCY WITHIN THE MIDDLE-SCHOOL MATHEMATICS CLASSROOM
23
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