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Article Excerpt
Imagine a series of mathematics professional development (PD) sessions. A group of teachers meets regularly. A skilled facilitator uses records of practice to lead thoughtful conversations. The teachers do mathematics together, analyze student work, and bring in examples or stories from their own classrooms. Observers might characterize these sessions as the kind of quality PD that should become normative in schools and districts across the nation. After sustained participation in these sessions, we observe teachers' classrooms and find dramatic transformations in the classroom practices of some and hardly a trace of the PD work in others. What should we conclude? The PD was not as good or effective as we thought it was. Some teachers "got it" more than others. Maybe the students resisted. Perhaps the goals were too ambitious and the teaching too hard. There could have been a lack of support in the school or district. Any of these explanations are plausible. Yet they all reflect a predominant view of thinking about teacher learning in unidirectional terms, one that understandably construes evidence of learning as implementation of new ideas in the classroom. We wish to disrupt this prevalent view and offer a new way of conceptualizing the relationship between teachers' experience in PD and their classroom practice. (1) We contend that researchers should examine whether and how teachers' participation across these settings coevolves over time by asking, "What is the relationship between settings over time, and how does this affect teachers' participation in each setting?" We show why pursuing that question instead of the more typical, "What is the impact of participating in PD on teachers' practice?" will strengthen how we understand and design for teacher learning.
Now picture two teachers who participated in the same series of PD sessions we sketched above. One of them, Lupe, came to each session with questions about what she tried in her classroom and gave detailed accounts of students' thinking. She left those discussions with ideas about what to investigate or experiment with next. Her participation in PD helped her rework her classroom practice, and her classroom practice helped her make sense of her engagement in PD activities. Over time, her work across these two contexts fed her efforts to figure out how to bring her students' ideas in more purposeful engagement with one another. Another teacher, Juan, also got ideas from the PD sessions that he tried in his classroom. He searched for worthwhile tasks that would help his students develop conceptual understandings of their computational strategies. He shared these strategies during PD sessions but provided less detail about what his students did and thought. In contrast to Lupe, his work in the classroom rested more on posing tasks and managing time rather than finding ways to bring his students' ideas into more purposeful engagement with one another. For Juan, his engagement across settings was more loosely coupled, whereas for Lupe her participation in one context propelled her participation in the other and vice versa.
It is precisely this relationship across contexts over time that is the focus of our article. Our argument is this: To better understand why and how some teachers' practice changes more than others while engaging in PD, we need to reconceive how we document and understand the learning that occurs. We develop our argument in the following way. First, we make a distinction between knowledge that is possessed and knowing that is deployed in action. Learning to improve teaching entails developing both knowledge and knowing. We carry this distinction into a review of how teachers' instructional practice is represented in professional education that centers on records of practice, paying particular attention to the relationship between individual and collective learning. We then make our case for the benefits of moving from unidirectional to multidirectional analyses of teacher learning across the PD and classroom contexts. We illustrate the idea of coevolution with a range of examples and end with recommendations for the design and study of PD.
Attending to "Knowledge" and "Knowing" Across Contexts in Research and Development Programs
Our work connects with recent attempts to map out the terrain for research on teacher learning and PD. Educational researchers have yet to build an empirical base to examine the mechanisms by which teachers' work in PD supports their classroom work and, we would add, vice versa (Borko, 2004; Lewis, Perry, & Murata, 2006; Wilson & Berne, 1999). We use our perspective to help us think about why and how some teachers transform their teaching more than others through participation in PD. This attention to the mechanisms for learning will allow researchers to develop deeper knowledge about the possible paths of participation that lead to the stance of inquiry and experimentation that Ball (1997) and many others have advocated that we cultivate in PD (e.g., Cochran-Smith & Lytle, 1999; Franke, Carpenter, Levi, & Fennema, 2001; Lampert & Ball, 1998).
Teachers are simultaneously involved in multiple activity settings (Wertsch, 1985), including their own classrooms, schools, and districts. When they are involved in sustained PD efforts, this constitutes another important mediating context. (2) We use the construct of activity settings to focus on the dynamic boundaries and relationships between settings and how those influence and explain teacher learning. To develop our ideas about studying coevolution across contexts further, and to specify a way of talking about learning, we draw on Cook and Brown's (1999) distinction between knowledge and knowing. (3) Knowledge, in their view, is something that we "possess" We "deploy" this knowledge in our actions. In their words, "Knowing refers to the epistemic work that is done as part of action or practice, like that done in the actual riding of a bicycle or the actual making of a medical diagnosis" (p. 387). Knowledge, then, can be seen as a tool of action because individuals or groups can use knowledge (whether tacit or explicit) to discipline their interactions with the world. This distinction seems both relevant and important in thinking about teacher learning.
Cook and Brown (1999) would agree that knowledge is essential for practice, but it is not sufficient for explaining what it takes to be good at what you do: "An accomplished engineer may possess a great deal of sophisticated knowledge; but there are plenty of people who possess such knowledge yet do not excel as engineers" (p. 387). In addition to all the kinds of knowledge that teachers need, among them, knowledge of the discipline, their students, and instructional strategies (Ball & Bass, 2000; Shulman, 1986), they also have to be able to teach. For us, this means that we have to attend to the interplay between knowledge and knowing in the PD context itself and in teachers' instructional contexts. We need to link the knowledge and ways of knowing that teachers develop as they work with colleagues in PD with what happens as teachers try to enact their learning in the context of their classroom teaching. Lupe and Juan may have developed similar ways of talking about students' mathematical thinking and similar knowledge of students' mathematical trajectories through the PD sessions, but their instructional practice changed in different ways. We clearly need to concern ourselves with how teachers draw on their knowledge when they interact with students or, in Cook and Brown's terms, how they deploy that knowledge in the service of knowing or disciplining action. Moreover, we argue that researchers should examine what teachers are learning during and after PD, looking at the coevolution of participation between classroom practice and PD. We claim that this coevolution between the PD and classroom contexts should itself be a key unit of analysis as we try to explicate the mechanisms by which teachers learn in and through PD.
We situate this article in the area of mathematics education for several reasons. Pragmatically, it reflects our own area of expertise and enables us to focus the examples we use. Although we contend that our argument is not limited to mathematics teaching and learning, mathematics education is particularly well suited to our purposes. The mathematics education community has strived for decades to specify the work teachers do to respond to and advance students' mathematical ideas. When student thinking is the center of instruction, teachers must learn how to (a) elicit and make sense of their students' mathematical thinking and reasoning, (b) choose and use mathematical tasks and representations that allow for productive and worthwhile mathematical learning trajectories, (c) orchestrate equitable classroom discussions and group work so that students productively engage with each other's ideas, and (d) monitor students' independent and group work to ensure that students develop conceptual and procedural understandings. To use Cook and Brown's terms, mathematics teacher educators are among the leaders in the field in experimenting with PD programs that are designed to support teachers to gain knowledge about what is entailed in enacting those core tasks of teaching and how to use that knowledge to further serve their teaching practice (knowing).
Practice-Based Professional Education (PBPE)
In mathematics education, researchers have articulated a vision for organizing professional education around records of practice, referred to as PBPE. Ball and Cohen (1999) outline key elements of PBPE, arguing that professional learning should (a) be centered in critical activities of the profession, (b) "emphasize questions, investigations, analysis, and criticism" (p. 13), and (c) make professional learning a more collective endeavor.
Centering professional education in practice is not a statement about either physical locale or some stereotypical professional work. Rather, it is a statement about a terrain of action and analysis that is defined first by identifying the central activities of teaching practice and second by selecting or creating materials that usefully depict that work (p. 13).
In Cook and Brown's (1999) terms, Ball and Cohen (1999) argued that we must create representations of the ways of knowing involved in teaching. The critical task for teacher educators, they argue, is to depict practice in ways that make it accessible to teachers. Ball and Cohen suggested this can be done through "strategic documentation of practice" (p. 14), carefully selecting and combining artifacts and representations, focal points for collective inquiry into practice.
In our brief review of the PBPE literature, we highlight the role teachers' classroom context has played in the design of PD that centers on records of practice. We note differences in (a) what Horn (2008)...
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