Understanding teacher learning

as changing participation in communities of practice

Elham Kazemi University of Washington ekazemi@u.washington.edu

Megan Loef Franke University of California, Los Angeles mfranke@ucla.edu

Abstract: This study investigates teachers’ learning trajectories as they studied their own students’ mathematical thinking. Teachers examined student work in monthly workgroups. Within a community of practice perspective, we analyzed different forms of participation across workgroup and classroom communities. We identified two forms of peripheral participation and one form of full participation, which we call generative. Teachers who moved towards generative participation experienced the workgroup and classroom communities as tightly linked and interactive. Their participation in the classroom altered the kinds of questions they raised in the workgroup, which in turn changed their participation in the classroom. In contrast, peripheral participants, while contributing to the development of the workgroup community, experienced their classroom community either as separate or as partially connected to the workgroup community. Implications for supporting teacher learning are discussed.

Teacher learning in mathematics is more than a matter of expanding knowledge and developing new pedagogical practices (Franke, et al., 1998). It is also an enterprise that consists of crafting and recrafting an identity about what it means to teach and learn mathematics. This study advances our understanding of teacher learning as developing identities through participation in communities of practice.

Theoretical Framework

We draw from the work of Lave, Wenger, and Rogoff to interpret learning within a community of practice perspective in which the construct of participation plays a central role. Lave and Wenger (1991) define a community of practice as “a set of relations among persons, activity and world, over time and in relation with other tangential and overlapping communities of practice” (p. 98). Lave (1996) describes learning as “changing participation in changing ‘communities of practice’” (p. 150). Learning is not a process of acquiring or transmitting knowledge. Rather learning is apparent in the way participation transforms within a community of practice. The shifts in participation do not merely mark a change in a participant’s activity or behavior, however. A shift in participation involves a transformation of roles and the crafting of a new identity, one that is linked to but not completely determined by new knowledge and skills (Lave, 1996; Rogoff, 1997; Wenger, 1998).

Method

The study took place at an elementary school in a small district in a large urban area in California. Eighteen teachers participated. Data were collected during the 1997-1998 school years. The student body, roughly 1300 students, was 90% Latino. Over 90% of the student body was on free or reduced lunch.

Teachers met in one of two monthly workgroups facilitated by the authors. Prior to each workgroup, they posed a similar problem (provided by the authors) to their students. The workgroup discussions centered on the student work those problems generated. The problems were drawn from research on the development of children’s mathematical thinking and focused initially on whole number operations (Carpenter et al., 1999). The goal of the workgroup sessions was to create frameworks for understanding children’s thinking that reflected teachers’ practical knowledge and current research knowledge (Richardson, 1990, 1994). The authors visited each teacher’s classroom at least once, and usually twice, between each workgroup meeting for purposes of data collection, professional support and continuity.

Data included initial and final teacher interviews, transcripts of workgroup conversations, student work, fieldnotes from classroom visits, and teachers’ written reflections during workgroup meetings. The data provided the basis for longitudinal case studies that unveil the diversity and shifts in individual participation across the workgroup and classroom communities.

Results

The workgroups developed as communities where teachers brought student work from their classroom, made public their classroom practices, and investigated the teaching and learning of mathematics. We traced different trajectories of participation across one year of workgroup meetings (the teachers have continued to meet, now into the fourth year). The forms of participation are described in relation to the goal of creating classroom communities where building on student thinking is central. These trajectories of participation allow us to examine the diverse ways teachers participated in the workgroups and in their classrooms and the implications for changes in teacher learning about student thinking and pedagogy. We identified three broad forms of participation that emerged and shifted across the year in predictable and meaningful patterns: two forms of peripheral participation and one form of full participation, which we call generative (see Figure 1). We describe the forms of participation by tracing how teachers used the workgroup problem, how they interacted with their colleagues in the workgroup and with their students in the classroom, and how they reflected on their experience during the year.

Figure 1. Shifts in participation for individual teachers during first year.

peripheral-A	Peripheral-B	Full/Generative
Elena (K, 0 yrs)
Yolanda (K, 0 yrs)
Javier (1, 14 yrs)
Beatriz (2, 7 yrs)
Miguel (1, 0 yrs)
Rosalba (K, 8 yrs)
Adriana (1, 3 yrs)
Paula (1,3 yrs )
Anna (3/4/5, 0 yrs)
Karen (1, 11 yrs)
Claudia (2, 0 yrs)
Jazmin (K, 8 yrs )
Laurie (1, 11 yrs)
	Rose (2, 3 yrs)
	Juan (1/2, 5 yrs)
	Kathy (3/4,0 yrs )
	Alma (3/4, 2 yrs)
	Lupe (4, 7 yrs)

Note: Names are pseudonyms. Grade level and years of teaching experience are designated in parentheses.

Italic = Teachers meeting in one workgroup; Bold = Teachers meeting in second workgroup.

Peripheral Participation -- A

A number of teachers’ participation remained peripheral in relation to the evolving purpose of the workgroup meetings. They attended workgroup meetings but did not buy in to the broader goals of developing their classroom practices in relation to students’ mathematical thinking. Peripheral-A teachers posed most if not all of the workgroup problems to their students, but the problems remained separate from the rest of their curriculum. They adapted the problems to make them easier for their students. The patterns of participation with their students remained the same throughout the year. Their lessons would begin with examples of how to solve particular problems followed by time for student practice. Teachers rarely elicited student thinking. When they did, they reported their frustrations about students’ inability to communicate their thinking. The teachers did not experiment with classroom participation structures that would allow students to solve problems using their informal strategies or to develop students’ ability to articulate their thinking.

Peripheral-A teachers proceduralized problem solving by modeling solution strategies. They viewed students’ informal strategies as unusual or more applicable to their bright students. They described the workgroup experience as not being very helpful either because they were unable to get the ideas they expected to or because the conversations did not add to what they already understood about teaching. The student work they shared, for the most part, fit with their expectations for student performance. They reported that many of their students were confused and unsuccessful in solving the workgroup problems. They also reported surprise when one of their struggling students was able to solve the problem. Their interactions with us outside of the workgroup were pleasant, and they rarely had questions about their students’ thinking or asked about how they could develop a dimension of their practice.

Peripheral Participation -- B

Another group of teachers also participated peripherally, but in a different way than the first group of teachers. This second group may have adapted the workgroup problem or posed it more than once, but the adaptations served as “warm ups” to expose students to the problem type. Other times, teachers were curious to see if their students would be able to solve the problem. The adaptations were only loosely tied to student thinking. In the classroom, teachers allowed students to solve problems using their own strategies, but they continued to model the problem first or step in with a strategy if a student was having difficulty. Teachers began to experiment with classroom participation structures. For example, teachers may have posed a problem and asked students to share their strategies.

In the workgroup context, peripheral-B participants regularly shared more than one student strategy. They did not question their practice to the extent of a generative participant (see below), though they were willing to experiment with the problem and devote a larger part of their curriculum to problem solving. At a general level, they expressed interest in the goals of the workgroup and found the experience to be helpful. In their interactions with us, they may have asked us for problems to pose and sought out suggestions about ways to structure their classroom discussions.

Full or Generative Participation

The generative teachers (Franke et al., 1998) were not all at the same level of mastery in appropriating and making use of a framework for children’s thinking. Rather, they were developing and shaping their identities as learners in both the classroom and workgroup settings. They used their emerging understanding of student thinking to purposefully adapt the workgroup problem several times. One adaptation would lead to another, each a means to gather information about student thinking. Generative teachers consistently brought student work to the meeting, sharing work that related to questions they were developing about mathematics or about student understanding. The student work and the workgroup conversations raised questions about a dimension of student thinking that teachers investigated further in their classroom.

In the classroom, generative teachers developed and experimented with ways to elicit students’ strategies. They allowed and expected all of their students, not just their most advanced students, to use informal strategies. Generative teachers learned about strategies that were unfamiliar to them through their students’ explanations. If a student was having difficulty, they tried to find a way for the student to use what s/he knew rather than impose a teacher strategy. In their informal interactions with us, teachers were eager to share “amazing” strategies. They wrote new problems to pose to their students but asked for our suggestions. We puzzled together over strategies they did not follow, and they had a growing concern with student understanding and next steps for instruction that would build their students’ thinking.

Discussion

Wenger (1998) claims that, “By its very practice, the community establishes what it means to be a competent participant, an outsider or somewhere in between” (p. 137). Generative participants were defining and establishing what full participation in communities centered on student thinking and professional growth would involve. Peripheral participants were possibly on an inward trajectory towards full participation to the extent that they were developing an ability and desire to identify and support their students’ mathematical ideas. Yet peripheral participants continued to divide their workgroup math from other math practices in their classroom. Generative participants allowed their students’ mathematical thinking to drive their experimentation in the classroom and their participation in the workgroup meetings.

As facilitators, our goal was to help teachers develop strong connections between the workgroup and the classroom. As we traced what happened over the course of the year, it was clear that all teachers did not gain the same benefit from their participation. What can we learn from this analysis? First, the data speak to the difficulty of transforming teachers’ knowledge and classroom practice within the course of one year. Clearly, change takes time, and schools and districts must be mindful of the length of time teachers need to engage in sustained work before significant changes become visible. As we have continued to work with the teachers, we have been able to document the benefits of continued professional development for both teacher and student learning. Second, our experience spending time with teachers across the classroom and workgroup communities underscores the difficulty of drawing on the workgroup experience in the context of classroom structures that conflict with the goal of eliciting and building student thinking. Teachers and students must learn new ways of experiencing mathematics class, which is not a small or trivial task. For many teachers, however, student work became an intriguing and powerful artifact that provided a purpose and direction to their emerging thoughts and practices (Wertsch, 1998). Finally, our vision of mathematics education remains a strong challenge to the status quo in schools, and developing school cultures that support teacher and student learning merits continued study.

References

Carpenter, T.P., Fennema, E., Franke, M.L., Levi, L., & Empson, S.B. (1999). Children’s mathematics: Cognitively Guided Instruction. Portsmouth, NH: Heinemann.

Franke, M. L., Carpenter, T., Fennema, E., Ansell, E., & Behrend, J. (1998). Understanding teachers' self-sustaining, generative change in the context of professional development. Teaching and Teacher Education, 14, 67-80.

Lave, J. (1996). Teaching, as learning, in practice. Mind, Culture, and Activity, 3, 149-164.

Lave, J., & Wenger, E. (1991). Situated learning: Legitimate peripheral participation. Cambridge, England: Cambridge University Press.

Richardson, V. (1990). Significant and worthwhile change in teaching practice. Educational Researcher, 19, 10-18.

Richardson, V. (1994). Conducting research on practice. Educational Researcher, 23, 5-10.

Rogoff, B. (1997). Evaluating development in the process of participation: Theory, methods, and practice building on each other. In E. Amsel & K.A. Renninger (Eds.), Change and development: Issues of theory, method, and application (pp. 265-285). Mahwah, NJ: Erlbaum.

Wenger, E. (1998). Communities of practice: Learning, meaning, and identity. Cambridge, England: Cambridge University Press.

Wertsch, J. V. (1998). Mind as action. New York: Oxford University Press.