# Communities of Practice in Mathematics Education

**DOI:**https://doi.org/10.1007/978-3-319-77487-9_25-2

## Keywords

Ethnomathematics Professional learning communities Social theory of learning Equity## Definition and Originators

Communities of practice (CoP) are an important component of an emerging social theory of learning. Lave and Wenger (1991) originally envisioned this social learning theory as a way to deepen and extend the notion of situated learning that occurs in traditional craft apprenticeships, contexts in which education occurs outside of formal schools (“Anthropological Approaches”). Drawing upon evidence from ethnographic investigations of apprenticeships in a range of settings (e.g., tailoring), they have frequently argued that it is important to separate learning from formal school contexts to understand that most human activities involve some form of teaching and learning. Wenger (1998) argued that three dimensions inherently connect CoP’s two components (community and practice): “1) mutual engagement; 2) a joint enterprise; 3) a shared repertoire” (p. 73). One important aim of a CoP is the negotiation of meaning among participants. Groups of people who live or work in the same location do not create a CoP unless they are actively involved in communicating with each other about important issues and working together toward common goals. Another important aspect of CoP is that learning may be demonstrated by changes in the personal identities of the community members. Changes in identity are accompanied by increasing participation in the valued practices of this particular CoP as newcomers become old-timers in the community.

## How CoP Connects to Developments in Theories of Learning Mathematics

Social theories of learning have a long history in psychology (Cole 1996). Nevertheless, more experimental and reductionist theories were the predominant form of psychology until the late twentieth century. The reemergence of social theories of learning has occurred in numerous places, such as discursive psychology (Harré and Gillett 1994), as well as in mathematics education (Lerman 2001; van Oers 2001). Sfard (1998) has outlined the reasons why we need a social learning theory in mathematics education. She contrasted two key metaphors: learning as acquisition versus learning as participation. Most research conducted during the last century in mathematics education used the acquisition metaphor. In contrast, the participation metaphor shifts the focus from individual ownership of skills or ideas to the notion that learners are fundamentally social beings who live and work as members of communities. Teaching and learning within CoP depend upon social processes (collaboration or expert guidance) as well as social products (e.g., tools) in order to help newcomers master the important practices of their community (“Theories of Learning Mathematics”). In addition, we need social theories of learning to address some of the fundamental quandaries of educational research and practice (Sfard 2008). These enduring dilemmas include the puzzling discrepancy in performance on in-school and out-of-school mathematical problems.

## History of Use

Lave’s (1988, 2011) own empirical research began with a focus on mathematical proficiency in out-of-school settings (e.g., tailoring garments). She initially chose situated cognition tasks that required mathematical computations so that she could more easily compare them with school-like tasks (“Informal Learning”). Other investigators in ethnomathematics conducted similar studies for a range of cultural activities (e.g., selling candy on the street) (Nunes et al. 1993) (“Ethnomathematics”). One recurrent finding of this research has been that children, adolescents, and adults can demonstrate higher levels of mathematical proficiency in their out-of-school activities than in school, even when the actual mathematical computations are the same (Forman 2003). Another finding was that social processes (e.g., guided participation) and cultural tools (e.g., currency) were important resources for people as they solved mathematical problems outside of school (Saxe 1991, 2012). This research forces one to question the validity of formal assessments of mathematical proficiency and to wonder how mathematical concepts and procedures are developed in everyday contexts of work and play (“Situated Cognition in Mathematics Education”). Many of these investigators began to question the basic assumptions of our individual learning theories and turn their attention to developing new social theories of learning.

Social theories of learning have had a greater impact on school-based research in the last 10 years. Research in teacher education, for example, has embraced the idea of CoP because it allows us to go beyond a bifurcated focus: either on individual teachers or on the organizational structure of schools (Cobb and McClain 2006; Cobb et al. 2003) (“Communities of Practice in Mathematics Teacher Education”). Cobb and his colleagues used an expanded version of Wenger’s (1998) CoP framework to view teachers’ practices as part of the “lived organizations” (2003, p. 13) of schools and districts (“Mathematics Teacher as Learner”). This expanded framework has allowed them to understand the multiple communities in which teachers and administrators participate (e.g., as mathematics leaders, as school leaders, or as members of a professional teaching group) (“Education of Mathematics Teacher Educators”). Each community may have its tacit norms and practices, requiring individuals to serve as brokers during boundary encounters and to create boundary objects that allow them to mediate between groups. Wenger (1998) argued that people create boundary objects through a process of reification. For example, boundary objects in teacher education can be common planning tools or agreed-upon student characteristics. Although boundary objects may not embody identical meanings for all groups of participants, they can allow for coordination of activity between communities.

As applications by Cobb and his colleagues of CoP to teacher education were widely disseminated in the mathematics education community, other investigators worked on expanding the theoretical and empirical knowledge base (“Professional Learning Communities in Mathematics Education”). For example, Bannister (2015) combined Goffman’s notion of frame analysis with Wenger’s CoP to conduct a microanalysis of changes in the pedagogical reasoning of one team of high school mathematics teachers over several months. Her analysis of ethnographic data focused on both participation patterns (e.g., turn taking) and reification (e.g., boundary objects such as “struggling students”) (“Discourse Analytic Approaches in Mathematics Education”). She was able to document distinct changes in the ways that this group of teachers characterized struggling students: from attending to static attributes to focusing on classroom interventions to support those students (“Frameworks for Conceptualizing Mathematics Teacher Knowledge”).

## Perspectives on Issues in Different Cultures/Places

The earliest research about CoP was conducted in diverse cultural settings: Brazil, Liberia, and Papua New Guinea (“Cultural Diversity in Mathematics Education”). In addition to a broad range of national settings, this ethnographic work focused on the mathematical reasoning that occurred in the daily lives of people outside of schools. More recently, research sites were located in schools in Europe or North America (e.g., Cobb and McClain 2006; Corbin et al. 2003). Thus, unlike many educational innovations, the study of CoP began in impoverished locations and later spread to wealthy settings.

## Gaps That Need to Be Filled

Forms of mutual engagement change over time within any community (Wenger 1998). Collective goals evolve as different interpretations clash and new understandings are negotiated. New boundary objects are created and modified, new vocabulary developed, and new routines and narratives invented when this happens. As investigators such as Cobb and others follow teacher communities of practice over periods of months or years, we are able to understand the tensions and struggles that occur in different school districts as they attempt to change teachers’ practices to be more standards-based. Their application of Wenger’s CoP has allowed them to keep a dual focus on the learning of individual teachers and the institutional constraints and affordances presented by their schools, districts, and government entities. This dual focus can be seen in the Railside School project, originally documented by Boaler and Staples (2008) (“Equity and Access in Mathematics Education”). After several years of successful implementation, Railside was derailed due to national policy changes that increased standardization and accountability requirements (Nasir et al. 2014). Thus, CoP provides a framework for confronting the realities of maintaining a successful teacher learning community over long periods.

Finally, several investigators in mathematics education are now asking us to transcend the limitations of the CoP perspective in order to understand race, power, and identity in mathematical practices. They refer to this expansion of CoP as the sociopolitical turn (Gutierrez 2013; Nasir and McKinney de Royston 2013). These authors draw on critical race theory to characterize the dynamics that occur during interactions among members of dominant (white, middle-class adults) and nondominant communities (working class parents and students of color) (“Urban Mathematics Education”). These investigators and others question the narratives in which the underachievement of students of color is an individual failure and not a systemic devaluing of their cultural capital. This new direction allows us to situate communities in economic and political hierarchies that serve to maintain the status quo of systemic inequality at individual and collective levels. And it may permit us to construct counter-narratives of positive identity development by recognizing the cultural funds of knowledge of these students and offering different ways to access the power of mathematics (Quintos et al. 2011) (“Language Background in Mathematics Education”). In their own way, these investigators are returning to the roots of CoP in situated practice in order to re-examine the enduring dilemmas of mathematics education.

## Cross-References

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