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Opportunities for Professional Learning in Mathematics Teacher Workgroup Conversations: Relationships to Instructional Expertise a

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Ilana Seidel Horn & Britnie Delinger Kane a

Vanderbilt University’s Peabody College Accepted author version posted online: 15 Apr 2015.

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Learning Outside of School Strand

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Opportunities for Professional Learning in Mathematics Teacher Workgroup Conversations: Relationships to Instructional Expertise Ilana Seidel Horn and Britnie Delinger Kane

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Abstract: Increasingly, instructional improvement efforts include teacher communities as part of their overall strategy, yet the relationship between teachers’ talk and professional learning

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remains underspecified. Using a discourse perspective on learning, this paper compares opportunities to learn (OTLs) in the collaborative conversations of three mathematics teacher

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workgroups. We examine the differences in OTLs in 17 hours of videotaped meetings from 3 groups at different levels of instructional accomplishment in secondary mathematics. Using

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mixed methods, we uncovered differences in the groups’ interactions and found that OTLs were not equally distributed. Instead, teacher groups whose active participants demonstrated the greatest facility with ambitious instruction also had the richest conversational OTLs. We interpret this as an accumulated advantage developmental story: because collaborative work in teaching involves problem posing and the articulation of practice, teachers’ conceptions get built into the framing and discussion of pedagogical problems. Accomplished teachers are thus

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Vanderbilt University’s Peabody College

positioned to learn more from talking with colleagues. This analysis contributes to our understanding of how OTLs are constituted in teacher workgroups, with implications for making better use of teacher collaboration for professional learning.

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Correspondence should be addressed to Ilana Seidel Horn, Vanderbilt University's Peabody College, Teaching & Learning, Box 230 GPC, 230 Appleton Place, Nashville, TN 37203. Email: [email protected]

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For several decades, sociologists of education have observed a consistent relationship between schools with strong teacher communities and higher-than-expected student achievement (Bryk et

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compelling and signal possible influences on teacher learning. For instance, teachers with strong communities are more likely to engage in ongoing improvement (Louis, Marks & Kruse, 1996),

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have access to expertise in teaching (Frank, Zhao & Borman, 2004), and develop student-

effective instruction.

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centered practices (McLaughlin & Talbert, 2007). Together, these may contribute to more

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As investigators probe these findings, explanations emerge for this improvement-orientation. Strong professional communities foster trust that supports teachers in the risk-taking necessary for developing new practices (Bryk & Schneider 2002, Bryk et al. 2010). Collegial conversations can create forums for teachers to share expertise and resources (McLaughlin & Talbert, 2001; Lampert, Boerst & Graziani, 2011). School-based teacher communities often enhance professional development (Wilson & Berne, 1999). Likewise, teachers’ conversations about

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al, 2010; Louis & Marks, 1998; McLaughlin & Talbert, 2001). The correlative relationships are

instruction support sensemaking around the meanings of new practices (Coburn, 2001), allowing for site-specific interpretations of general ideas. Also, the interactional routines in collegial discussions orient teachers toward problems of practice, potentially creating opportunities for learning (Horn & Little, 2010).

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To be sure, it is now a well-circulated assumption that teacher communities can enhance professional development. The National Staff Development Council, the largest non-profit professional association for staff developers in the United States, recently included “learning

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communities” as one of their twelve professional standards for quality staff development (NSDC, 2011). The Canadian province of Alberta passed legislation to mandate professional

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system. Indisputably, professional community has become part of the current educational zeitgeist.

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However, not all workgroups –– our term for gatherings of teachers charged with collaborative work, whether or not they consider themselves a community –– are equally

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generative for teacher learning. Just as pushing student desks together does not in itself make for

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effective cooperative classroom learning, neither does granting teachers shared planning time necessarily make for effective workplace learning. These efforts to influence the quality of teachers’ interactions by merely making space for them to occur reflect what Little (1990) long ago called the “optimistic premise of teacher community.” In fact, the capacity for deep collaboration among teachers remains questionable. A

survey conducted by Public Agenda found that only 20% of high school teachers reported that

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learning communities in schools (Hargreaves, 2007), as has the New York City Public School

they “regularly meet to share ideas about lesson plans and methods of instruction” (Public Agenda, 2002, p. 23). Given the paucity of mere idea sharing among teachers in the recent past – – an activity which does not approach the complexity of collaborative pedagogical problem solving (Horn, 2010) –– typical school cultures may not yet be ripe for the kind of collaboration

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that supports transformative learning. Cultural change is slow, and the norms of privacy that have prevailed for decades are still likely to shape teachers’ workplace culture (Little, 1990). Professional culture is, of course, not the only impediment to meaningful collaboration.

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Structural obstacles are nontrivial: overfull schedules force school leaders and teachers to contend with competing demands on their time. Secondary teachers typically have upward of

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demands of planning, grading, and parent communication. In many improvement-oriented schools, additional meetings outside the contracted workday strain teachers’ capacity (Bartlett,

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emotion that collaborative work requires.

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2004). These organizational conditions work against the investment of time, intellect, and

Given these reasons for both optimism and caution about teacher workgroups as a support for

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teacher learning, research and practice would benefit from a clearer account of how conversations contribute to professional learning. Pragmatically, such analysis stands to bolster in-school teacher workgroups and enhance professional development efforts. Theoretically, understanding this complex phenomenon contributes to studies of workplace learning. To this end, we present a comparison of three teacher workgroups participating in a professional development project designed to improve high school mathematics instruction.

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150 daily student contacts with a 50-minute preparation period, which is already taxed by the

Our study design reduced the organizational and cultural conditions that might differentially support effective workgroup collaboration, allowing us to hone our analytic lens on the interactional processes of learning as they relate to varying levels of teacher accomplishment. Organizationally, all three workgroups were given an extra daily planning period for their

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collaborative work so as not to impinge on other demands on their time. To support positive collaborative cultures, the groups were comprised of volunteer teachers who were financially compensated for their participation in intensive, high quality professional development. To

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provide in situ expertise, a knowledgeable instructional coach regularly facilitated each group. At the same time, the teachers’ varying levels of accomplishment in ambitious mathematics

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opportunities for learning in their collaborative conversations.

This paper contributes a discourse analysis of teacher workgroup learning. Our theoretical

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framework synthesizes insights from prior work on teachers’ workplace learning, with a focus on discourse features that contribute to that learning. In addition, we introduce new data analysis

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methods to provide an in-depth qualitative and quantitative comparative analysis of our cases.

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Theoretical Framework: Teachers’ Opportunities to Learn in School-based Workgroups Learning in Teacher Workgroups. To develop our theoretical framework, we draw on extant literature on teacher workgroups and reinterpret it from a learning perspective. In this vein, we

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instruction proved important for understanding how their current understandings shaped the

do not make claims about how participation in workgroups influenced any individual teachers’ learning. Rather, we look at how the conversational milieus provided differential access to professional knowledge for workgroup participants. In a sense, we are looking at how workgroup conversations operate as a collective zone of proximal development (ZPD) for teachers (Engeström, 1987). Workgroup interactions frequently delineate what is possible for participants.

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Sometimes, for instance, participants expand their sense of what is possible, which Engeström (1987) has characterized as expanding the collective ZPD. Adults guide much of their own development of practice, and images of what is possible contribute to what they even attempt,

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along with the details of how they might undertake different practices. Tracing the organization of discourse and how it provides critical conceptual resources for understanding mathematics

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sociocultural system, render a collective ZPD that sets the stage for future learning.

Opportunities to Learn. To capture the nature of that learning, we use opportunities to learn as a

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leading construct. Greeno and Gresalfi (2008) describe opportunities to learn as:

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affordances for changing participation and practice. In this view, understanding a learner's trajectory involves hypotheses about affordances that are available to the learner to participate in

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particular ways. (p. 172)

Our “hypotheses about affordances” in workgroup conversations lead us operationalize opportunities to learn in workgroup conversations by examining how interactions: (1) marshal conceptual resources for teachers and (2) mobilize them for future work (Hall & Horn, 2012). We analyze workgroup talk for how it provides conceptual resources, organizing interpretations of past and future teaching, and the ways these resources connect to teachers’ subsequent work.

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teaching, both in the past and future, is one way of understanding how teacher workgroups, as a

We note that teachers are often thought of as “doers” more than “thinkers” (Feiman-

Nemser, 2012). Commonplace images of teachers in the act of instruction overshadow the important (albeit invisible) thinking that happens before, during and after lessons. However, as

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has been argued elsewhere (e.g., Horn, 2007; Skott, 2009; Thompson, 1984), teachers’ conceptions about their work are highly consequential for their instructional decision-making. Understanding how these concepts underpin and become reinstated in teachers’ interaction is

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therefore a worthwhile topic of study. Concept Development in Teachers’ Talk. In our framework, teachers’ talk supports the

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and lived (“spontaneous”) concepts (Vygotsky, 1987). Formal concepts might be encapsulated through instructional terms, such as smartness or assigning homework. The lived concepts reflect

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the meanings attached to those ideas. Through this dialectic of language and experience, teachers’ meanings about particular ideas or practices are socioculturally situated, arising out of

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interchanges with other people in their social world. As interactions around these words accrue

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over time, teachers identify certain students as displaying smartness or develop particular ways of assigning homework in negotiation with a constellation of culturally specific values and practices, thus developing their understanding of teaching concepts. Horizons of observation and asynchronicity. Workgroups become fruitful places to examine the development of teaching concepts because, in the US, teaching is still largely individual work. Thus the concrete particulars teachers encounter around any given concept typically only occur

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development of teaching concepts through an interplay between formal (“scientific”) concepts

in the privacy of their classroom. Consonant with the collective ZPD (Engeström, 1987) notion, workgroup conversations stand to shape teachers’ horizons of observation (Hutchins, 1995), narrowing or broadening their access to important facets of their work through discussions with colleagues. Horizons of observation

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describe the aspects of practice that are available for individuals to see and experience in different contexts. To draw on a familiar example, when apprentice tailors work within sight of more accomplished tailors, co-observing the construction of the same pair of trousers, this

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provides them with repeated access to details of the process (Lave, 2011). Horizons of observation thus constrain or expand what can be learned, since learners need to access practice

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However, in contrast to settings like Lave’s apprentice tailors or Hutchins’ ship navigators, a distinct conundrum arises when teachers try to learn in workgroups. Their conversations are

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necessarily asynchronous from the complex interactive work of classroom instruction. This asynchronicity shapes OTLs in teachers’ conversations in both positive and negative ways. On

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the plus side, the absence of the pressing immediacy of classroom activity gives teachers time to

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slow down the rapid decision processes instruction demands (see e.g., Grossman et al., 2009) and reflect on their work. At the same time, this asynchronicity limits the horizon of observation, requiring teachers to reconstruct relevant aspects of the classroom to bring under collective scrutiny. Asynchronicity heightens the role of talk in fostering shared meaning in teachers’ collective learning, so we attend carefully to teachers’ interactions and use of representations of the classroom in our analysis of teachers’ OTLs.

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to become more accomplished.

Conceptual Resources in Teachers’ Collegial Talk. So far, we have argued that concepts in teacher workgroups’ collective ZPD develop through the interplay between spontaneous and scientific concepts in their talk, changing the sense of the possible. Because workgroup talk and classroom instruction are asynchronous, teachers have limited horizons of observation onto each

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other’s work, so the conceptual resources constituted within workgroup talk require particular attention. Prior work on teacher workgroups identifies three conceptual resources that shape OTLs: representational means and practices, problem framing, and epistemic stances. We

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explain each of these below. Representations and representational practices. The OTLs in any context rely, in part, on

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health sciences or in physics, standardized representations such as statistical tables (Hall, Wright, & Wieckert, 2010) or time-distance graphs (Ochs, Gonzalez & Jacoby, 1996) stabilize

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experimental work for collective examination, shaping a group’s sensemaking. Representational practices refer to the ways people use these artifacts to interpret the world. Standardized

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representations coupled with common representational practices affix knowledge in ways that

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support shared interpretations across people, time, and contexts within a profession. Representations in teaching vary in their use and their specific details (Little, 2003). While there may be commonplace representations in teaching, such as textbooks or test score reports, there are not common representational practices for using these. This leaves teachers to develop local practices for using these representations, such as looking at a textbook a unit at a time versus looking at a textbook a lesson at a time. In addition to material artifacts, Horn (2005, 2010)

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representations to build collective understandings of practice. For instance, in research in the

identified a commonplace talk-based representational practice where teachers conversationally reconstruct classroom events. These serve to compensate for asynchronicity and specify the meaning of more generic observations about teaching. Replays recall past instructional interactions, while rehearsals generally anticipate them (Horn, 2010). Since this representational

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practice is highly local, teacher workgroup conversations provide different bases for developing collective understandings that are not necessarily shared across the profession. There are two points to make about this variability of representational means and practices in

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relation to teachers’ OTLs. First, even when representations of teaching are stabilized through

published curricular materials or teachers’ guides, they do not transparently point to similar

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constructed through these representations, they rely on teachers’ abilities to notice (Sherin & van Es, 2009) and articulate the work of teaching to shape the conceptual resources that constitute

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OTLs. Second, conversational representations such as reflective talk, rehearsals, and replays are highly dependent on teachers’ facility at reconstituting moments in or features of their

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classrooms. Finally, workgroup norms inform what aspects of teaching receive attention––what,

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exactly, is shareable. Do teachers only share triumphs with their colleagues or do they also share trouble? As the following sections describe, teachers’ representations of the classroom interact with—and are constituted by—teachers’ instructional problem framings and epistemic stances on their work, all mediated by workgroup norms. In combination, these resources inherently delimit the scope of any inquiry into practice from the outset of collective problem solving, thus shaping OTLs.

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interpretations of teaching and learning. While instructional problems may be partially

Problem framing. Discourse analysts use the idea of frames to describe how speakers define issues through activities and interactions (Goffman, 1974). In teacher communities, frames organize teachers’ collective attention, shifting the meaning of activities (Coburn, 2001; Horn, 2007), differentially positioning teachers as agents in the problems they face (Bannister, 2015;

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Horn, 2010), and, as a consequence, influencing opportunities to learn from conversations. For example, a common problem teacher workgroups face is the question of what to teach next. Some workgroup norms for instructional planning support a quick glance at teacher guides,

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followed by minor pacing adjustments. In these groups, OTLs are qualitatively different than in groups where the same question invites a prolonged reflection on students’ current

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planning as pacing frame shapes the first hypothetical group’s interactions, while a planning as building off of students’ current understanding frame shapes the second. Each engages reflection

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on teaching at consequentially different grain sizes and toward different ends. Likewise, issues of teacher agency influence the details of future work. If, for instance, teachers’ frames position

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them as having no actionable response to disengaged students, their future work will not likely include any specific strategies for addressing student motivation. In contrast, teachers who

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invoke frames that position them with agency around student motivation are likely to spend more time detailing those plans, providing conceptual resources for that future work (Bannister, 2015; Horn, 2007).

Epistemic stances. An epistemic stance is a position on what can be known, how to know it, and why it matters for teaching, learning, and mathematics (Hall & Horn, 2012). Both representations and frames interact with (and constitute) workgroups’ epistemic stances, as

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understandings of the material and their relationship to the key concepts in upcoming lessons. A

epistemic stances are delineated through talk. Sometimes the very organization of a workgroup context conveys stance: discussing instructional issues with a multidisciplinary grade level team, for instance, may communicate a different assumption about what is worth knowing than holding the same conversation with a single-subject grade level team. At a finer grain size, teachers may

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assert epistemic claims, or bald statements about what is worth knowing, how to know it, or why it matters. Whether at the level of activity or utterance, epistemic stances are conveyed, negotiated, and reinstated through the language teachers use to communicate about their work.

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Language is thus both a means for representing and for understanding problems of practice. Vygotsky famously conceptualized the relationship between talking and higher order thinking,

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Each word is […] already a generalization. Generalization is a verbal act of thought and reflects

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reality in quite another way than sensation and perception reflect it (1986/1934, p. 6). Thus, words—which can both represent and interpret problems of practice—act as

models and seeks to resolve.

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generalizations. In brief, language carries with it epistemic stances on the very problems it

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Summary of Theoretical Framework. We see teachers’ workgroup talk as constituting a collective ZPD and providing important conceptual resources for a shared sense of the possible – – what we call opportunities to learn (OTLs). The asynchronous nature of workgroup conversations requires teachers to reconstitute events beyond a shared horizon of observation, necessitating them to represent classroom events that have happened or will happen. By relying primarily on language as a medium to interact with artifacts, constitute representations, and

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claiming:

convey questions about teaching, teachers’ talk about instruction also conveys problem frames and epistemic stances about the nature of teaching. These different conceptual resources –– problem framings, representations, and epistemic stances –– provide substantively different

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traction on instructional problem solving, and, we claim, teachers’ OTLs. Our terms for conceptual resources in teachers’ talk are summarized in Table 1. In the following analysis, we show how language plays a variety of roles in teachers’ workgroup

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conversations, responsible for both representing and interpreting the work of teaching. The dual role of language leads to a paradox in teachers’ workgroup learning: Those whose workgroups

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conversations. This developmental pattern has been observed in other settings and called a

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Matthew Effect, invoking the Christian gospel, often shortened to the maxim that “the rich get richer” (XXV: 29). In a developmental context, whether referring to scientists making

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discoveries (Merton, 1968) or children learning vocabulary during independent reading (Stanovich, 1986; Walberg & Tsai, 1983), the Matthew Effect describes development

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characterized by accumulated advantage, wherein people with advantageous prior experiences are able to leverage new learning events more effectively. Based on our findings, our central claim is that teachers’ unfacilitated workgroup conversations provide another instance of accumulated advantage. Workgroups whose active participants are more accomplished in ambitious teaching tend to have conversations invoking richer conceptualizations of instructional issues and linked to specific future work. In the details of

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include active participants with rich conceptions of teaching end up with rich OTLs in their

their discourse, they have productive epistemic stances and pose problems that push on collective thinking about current practice. They deploy frameworks for instructional issues that provide them with agency, supporting conversations that reason through facets of a problem and consider alternative viewpoints. They also exploit the representational affordances of language to render

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and interpret key features of the classroom in ways that stand to deepen collective understanding of teaching and learning. With these advantages, workgroups with actively participating accomplished teachers provide greater opportunities for professional learning. The nature of our

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analysis assumes that OTLs arise through group interaction and are therefore created by and within a group, constituting a collective ZPD. Although individuals may hold and act on

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interaction by shaping the discussion.

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The Study

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Research Context: The Adaptive Professional Development Project The Adaptive Professional Development (APD) project was a six-year effort to increase access

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to and rigor in secondary mathematics through intensive professional development. Working in high schools in an urban district in the Pacific Northwest, the APD project focused on helping mathematics teachers use a form of collaborative learning called complex instruction (CI; Cohen & Lotan, 2014; Horn, 2012) through intensive and multifaceted professional development. CI involves redesign of both academic tasks and student participation. By focusing on rich tasks that involve multiple skills, teachers can more reasonably assume that no student is equally

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differing epistemic stances, the stances that support OTLs are those that prevail during group

competent in each of them, but that collectively the group can pool its abilities and make progress. Leveraging this interdependence, teachers then structure groupwork to teach high-level thinking, as each student within a group makes significant contribution to the solution of the problems. We focused on CI as an ambitious form of teaching (Lampert, Boerst, & Graziani,

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2011) because it aims to engage a broad range of students in rich representations of content. Additionally, prior research suggested that CI could improve mathematics learning and increase equity (Boaler & Staples, 2006; Cohen & Lotan, 2003).

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Although this analysis brackets off the particulars of the project in its focus on OTLs in teacher

workgroups, we provide a brief overview of APD to give a sense of the aims, scope, and values

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teachers’ development. APD activities were conceptualized as building toward improving instruction in teachers’ classrooms and fostering school-based professional communities.

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Learning activities for all teachers included a summer retreat at the Park City Mathematics

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Institute, workshops in the CI pedagogy, and monthly video clubs (Sherin & van Es, 2009). Once teacher groups made a commitment to work more intensively on CI, we worked with

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school leaders to build collaboration time into their daily work, providing weekly coaching for the workgroup, as well as weekly in-class coaching for individual teachers. At this level of mutual commitment, teacher groups became full participants in the scope of the professional development work. It is important to note that we formed these site-based workgroups only as departments expressed interest and readiness. Teachers are adult learners, and, unlike coming to class without a lesson plan, there are no professional sanctions for opting out of professional

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of the project. We worked with school and district leaders to create conditions to support

development activities. In our theory of action, teachers needed a desire to improve before our efforts would be meaningful for them. Daily collaboration time is a considerable investment, monetarily and organizationally, and we sought some kind of stated commitment from them before we helped them with these resources.

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Research Design The APD project became a place to examine the possible contribution of teachers’

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workgroups to professional learning. While there are many stories to tell, we focus this paper on

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the following question: How do conversational opportunities to learn compare in mathematics

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research sub-questions emerged as our analysis progressed in uncovering the nature of teachers’ workgroup conversations and their relation to learning opportunities. We specify these research

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sub-questions in our description of each phase of analysis below.

Additionally, note that we are not asking the usual question about the effectiveness of our

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professional development work. Instead, we are invoking the situated perspective and trying to understand the workgroups’ contribution toward the overall goal of teacher learning in this larger

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project. Using a comparative case study design (Yin, 2008), we looked at video records from the 2008-2009 school year of three teacher workgroups. Our purpose was to understand how their interactions differentially supported teachers’ opportunities to learn. The data lend themselves to a productive comparison of OTLs in workgroup collaboration since all three groups were in demographically similar schools and shared district and professional development contexts. At the same time, a naturally occurring cross-section of teacher expertise provided analytic purchase

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teacher workgroups at different levels of instructional accomplishment? As we will describe,

on the relationship between accomplishment in teaching and OTLs in workgroups. Teacher expertise was determined through observational rubrics designed by the project’s coach and facilitator, which are described in more detail in a later section.

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As our theoretical framework suggests, we examine teachers’ OTLs by looking at representations of practice, problem framings, and epistemic stances in the three workgroups’ conversations. Our claims rest on an analysis of how these provided conceptual resources for

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teachers’ sensemaking and the extent to which they informed teachers’ future practice.

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We focus this analysis on workgroups in three urban high school mathematics departments who had, to varying degrees, participated in ongoing, intensive professional development activities

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with the APD project. All three were located in the same urban school district in the Pacific Northwest of the United States. Teachers became full participants in the APD work on different

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timelines. Our case selection was thus opportunistic, reflecting the mutuality of engagement between the research team and the teachers. The three focal workgroups had adopted CI to

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different extents, allowing for an examination of potentially related differences in their talk. In annual interviews, all teachers reported their on-site collaboration time was critical to their individual professional growth. As in other studies of teacher collaboration, they reported that workgroup conversations provided a sense of emotional support and accountability as they made sense of new pedagogies in their classrooms.

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Focal mathematics departments and teacher teams

Workgroups as settings for teacher learning. We take facility with ambitious mathematics instruction as a starting point for our analysis, tracing out to the learning opportunities within groups whose participants differed in their enacted understanding of this pedagogy. Because the workgroups shared the same district context and professional development activities, we felt more confident that the differences in teachers’ workgroup talk could be attributed primarily to

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the differences in their accomplishment in ambitious instruction and not simply to other contextual differences. While differences in experience, personalities and group dynamics certainly existed, we sought confirming and disconfirming evidence about our claims relating

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teacher accomplishment and conversational OTLs within each workgroup, refining and supporting our overall findings. Thus our primary design was cross-sectional, but we used

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Our cross-sectional theorizing came from the instructional coach’s sense of individual teacher’s development in the target pedagogy. The coach brought practical and theoretical expertise to her

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work. Aside from her accomplishment in using CI as a classroom mathematics teacher, she researches teacher development and works as an in-service teacher educator. The instructional

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coach had strong rapport with the teachers, and, in our annual interviews, they all reported that

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her work with them was useful and effective. They described how she supported their ongoing learning, accelerating their development through constructive feedback in and out of the classroom. Across the board, the teachers were eager for the coaching and reported that it furthered their learning goals.

At the principal investigator’s request, the coach developed rubrics to locate the teachers’ development along different dimensions of CI practice in their classroom instruction. Categories

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within-group longitudinal data to refine our claims.

included assessments of student-to-student talk, inclusivity of student talk, students’ shared commitment to groupwork, and expanding notions of mathematical smartness. Using these emic categories, we classified the three groups as, on the whole, Beginning, Emergent, and Sophisticated in their CI practice. As Table 2 shows, variation existed within the groups, but we

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use these labels since the majority of participants fell in these categories. We note which participants were most active in the workgroup discussions, as this seemed consequential for OTLs, a point we will return to in the Limitations of Findings section at the end of the paper. We

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also provide a general sense of their teaching experience (≥ 5 years) and participation in the APD professional development offerings in tertiles (hours of participation/possible hours; high,

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since attendance was not feasible for all teachers and would distort the denominator.

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Focal data

To investigate OTLs in teacher workgroup conversations, this paper focuses on 14 videotaped

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collaborative teacher meetings from the 2008-2009 academic year. We contextualize our understanding of these meetings through a rich longitudinal data set of the APD project. Through

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active participation in the teacher groups and in professional development activities over six years, we collected hundreds of hours of fieldnotes, annual interviews with teachers, video recordings of classrooms, student achievement data, and recordings of teacher collaboration meetings.

To sample teacher workgroup conversations, we filmed each group of teachers repeatedly over

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medium, low) excluding the 3-week residency at the Park City Summer Mathematics Institute,

the course of the school year. The three groups had daily scheduled collaborative planning periods during their contracted work time. In our videotaped data set, the project coach facilitated six of these meetings. Eight meetings were unfacilitated. Although we coded all 14 meetings, we ultimately focused on the unfacilitated sessions because these provided a handle on

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the groups’ independent capacity for collaborative talk about teaching. Additionally, in our initial coding, we found that the discourse in conversations facilitated by the instructional coach showed much less difference across the groups, instead resembling the talk of the Sophisticated

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Group. We interpret this as a signal that the coach modeled expertise in collaborative teacher talk, corroborating our findings.

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importance of teaching for mastery); debated instructional goals (e.g., teaching graphing as a skill versus teaching graphing as a representation of concepts); or shared teaching approaches

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(e.g., how to use a poster project to showcase the mathematical “smartness” of more students).

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Analyzing differences in collaborative talk

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Using inductive, constant comparative methods (Strauss & Corbin, 1998), we analyzed the videoed conversations in four iterative phases, using the constructs from our theoretical framework to identify key differences in the workgroups’ discourse. The goal of each phase was to refine our understanding of how these differences in conceptual resources might distinguish OTLs in the workgroups’ talk. Anything that emerged as significant in one phase was noted and picked up in subsequent phases.

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Across the groups, meeting topics included discussions that asserted pedagogical values (e.g., the

We used StudioCode analysis software, allowing real-time coding while viewing video data, so we did not have to rely on transcripts to compare conversations within and across groups. This technology preserved the details of interaction and allowed for easy retrieval and quantification of coded video. The video coding software allowed for simultaneous qualitative and quantitative

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analysis, allowing us to make a new contribution to research on teachers’ conversational learning. We will describe the unfolding logic of our inquiry by detailing the purpose of each phase of

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analysis in the following sections and the sub-research questions that emerged, which was informed by the previous phase. Although we describe these phases linearly, we made

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analyses (Strauss & Corbin, 1998).

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Phase 1: Locating and measuring episodes of pedagogical reasoning. In this phase, we wanted to compare the time and attention each of the 3 workgroups devoted to discussing problems of

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practice. Thus the research sub-question informing this phase of analysis was: RQ1: What were the differences in (a) percentage of meeting time and (b) length of time that

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each group spent reasoning about their teaching during their conversations? This phase involved data reduction by focusing on interactions that might best yield an

understanding of the teachers’ OTLs in the different workgroups. Within the unfacilitated meetings, we looked for moments of teachers’ conversations that centered on problems of practice. Thus our primary units of analysis were episodes of pedagogical reasoning (EPRs)

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refinements to earlier phases as our findings emerged in later phases, as is common in inductive

(Horn, 2005), the moments of teacher-to-teacher talk where issues or questions about teaching practice are brought out and accompanied by some elaboration of reasons, explanations, or justifications. In our OTL framework, EPRs point us to the posing, framing, elaboration, and representations of instructional problems. EPRs can be single turn utterances, such as, “I’m not

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using this worksheet because it bores the kids.” Multi-party EPRs, in which descriptions of practice and pedagogical reasoning are co-constructed over many turns at talk, are more relevant to group development. To find the boundaries of EPRs, we looked for topical coherence. Often,

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teachers would begin an EPR with a question or broad statement, which the workgroup would then explore.

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minutes. We disaggregated these measurements by group, identifying the differences in

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percentage of time spent in EPRs (RQ1a) and length of EPRs across the groups (RQ1b). Phase 2: Looking at conceptual resource differences across the groups. Using constructs from

groups’ conversations. We asked:

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our framework, we sought to locate contrasts in the discrete conceptual resources in the different

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RQ2a: Which conceptual resources distinguish the teacher workgroups’ conversations during EPRs?

RQ2b: With what frequency are these resources deployed across groups? These questions sought to specify how the use of conversational resources, such as representations and epistemic claims, might distinguish among the groups as a way of

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This unit of analysis reduced 17 hours and 30 minutes of video data to about 12 hours and 11

understanding differences in OTLs. We focused on these conceptual resources as they could be coded in discrete conversational moments. (The less time-bound conceptual resources, epistemic stances and problem frames, were coded in Phase 4.)

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To code representations, we looked for interactions around curriculum artifacts, student work, use of technical teaching language, and stories of classroom talk. This last category focused on both replays and rehearsals (Horn, 2005, 2010). Teaching replays are blow-by-blow accounts of

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classroom events, while rehearsals are generalized or anticipatory versions of the same. Because perspective-taking during EPRs might indicate sophistication (Horn, 2010), we also coded

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teacher voices. More generally, we coded as representations of the classroom descriptions of classroom events that did not narrate specific voices. We also coded for technical language as a

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form of representation, since the use of such language has been linked to group development (McLaughlin and Talbert, 2006), attending to both CI language and other specialized teaching

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language. To code epistemic claims, we looked for propositions that served as the foundation for a chain of reasoning in teachers’ conversations. As described in our framework, these claims

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point to what is knowable about teaching and how to know it. Quantitatively, StudioCode allowed us to count and compare the frequency of the different codes across the data set (RQ2b). Qualitatively, it allowed us to review compiled movies of each code by workgroup. That is, we could view every instance of a workgroup’s use of representations to get a holistic sense of tone and meanings conveyed during these moments in their talk. From this within-code viewing, we saw that, in addition to the distinguishing quantitative differences

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replays and rehearsals for multivocality, replays or rehearsals that represent both student and

across the groups, the epistemic claims revealed the greatest differences in tone and meaning across the teachers’ conversations (RQ2a).

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Phase 3: Looking closely at epistemic claims about teaching. In this phase, our research subquestions focused on epistemic claims in the teachers’ EPRs since these conceptual resources

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RQ3a: What was the complexity and content of each group’s epistemic claims?

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seemed to most strongly distinguish the workgroups’ conversations. Our questions were:

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RQ3c: How often did each group link epistemic claims to representations?

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As the primary window into the teachers’ collective thinking about students, teaching, and mathematics, coding epistemic claims provided insight into the differences in OTLs in the

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workgroup conversations. Although individuals within groups certainly stated outlying epistemic claims, a set emerged that characterized the prevailing epistemic stance of each workgroup.

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To determine the complexity and content of each epistemic claim (RQ3a), we transcribed or paraphrased all epistemic claims and categorized them according to type, coding them for their focus on teaching (T), students (S), mathematics (M), or any combination of the three. For example, we identified the following epistemic claim and coded it T-S: Being consistent with routines helps students understand what behaviors are important for them to do. This statement asserts that teachers’ consistency with routines benefits students, which is why we code both T

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RQ3b: What kinds of epistemic claims did each group invoke and with what frequency?

and S; however, there is nothing in the claim that is specific to mathematics. We reviewed ambiguous epistemic claims in the larger conversational context and interpreted accordingly, making as little inference as possible from the teachers’ language.

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We then sorted epistemic claims according to their complexity. Claims about only one of students, teaching, or mathematics (S, T, or M) were coded as one-dimensional. Twodimensional claims include those coded as student-teaching (S-T), student-math (S-M), or

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teaching-math (T-M), while three-dimensional claims invoked all three at once (S-T-M). We tallied the distribution of the differently dimensional epistemic claims by workgroup, considering

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Looking at StudioCode’s coding window, we noticed that the Sophisticated Group’s epistemic claims to representations of practice appeared to co-occur with greater frequency than the other

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two groups. In our theoretical framework, this would signal the coming together of two different conceptual resources in teachers’ conversations. We investigated this by using the software’s

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cross-tabulation feature and counted the co-occurrences of these two codes (RQ3c).

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Phase 4: Interpreting the differences in OTLs in comparable EPRs. Through these analytic phases, we developed an understanding of how the conceptual resources in workgroups’ conversations were differently organized across the data corpus. With these fine-grained analyses as a backdrop, we then asked:

RQ4: How do these differences in conceptual resources shape OTLs in the workgroups’ interactions?

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the frequency of epistemic claims’ content (S, T, M) and complexity within each group (RQ3b).

This question allowed us to investigate how our findings in Phases 1-3 might shape the learning affordances within the workgroups.

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To this end, we examined similar episodes across the groups to understand how differences in conceptual resources –– the findings from Phases 2 and 3 –– contribute to OTLs. For each group, we selected and transcribed one or two consecutive EPRs from meetings in May

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2009. The EPRs were the most directly comparable in our data set since the teachers led with a shared (and common) problem: curriculum pacing and coverage at the end of the academic year.

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across the 3 workgroups to compare OTLs and relate them to interactional organization. This final phase enabled us to check our suppositions and to create a summary of our overall findings.

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Findings

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we report our findings.

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Table 3 below summarizes these phases of analysis to help readers follow the logic of inquiry as

When we looked across the three workgroups, who were, on the whole, at different levels of instructional accomplishment, we found three main differences in the groups’ collaborative talk. First, teachers with greater facility in ambitious practice spent more time discussing problems of practice. Second, the most accomplished teachers frequently considered broad ideas about teaching in light of local particulars. Finally, the most accomplished teachers more frequently

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We looked at how epistemic claims and representations worked in the context of sensemaking

considered students’ experiences and perspectives. These differences, we argue, provided teachers with different conceptual resources to interpret teaching problems and plan future work. In our framework, these differences supported richer opportunities to learn.

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We present our findings in two main sections. We begin by describing the results from Phases 13, findings that characterizes the organization of conceptual resources across the data corpus. Second, through the close analyses of interaction in Phase 4, we show how these differences

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shaped OTLs in the three groups.

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in Workgroup Conversations

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Finding 1: Time spent on problems of practice increased with sophistication in ambitious practice. During our data reduction phase, we measured the portion of total meeting time each

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workgroup devoted to problems of practice. We found that both the Sophisticated and Emergent Groups spent significantly more time discussing problems of practice than did the Beginning

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Group (almost 100% vs. 60%). In addition to spending more time together reasoning about practice, the Sophisticated and Emergent Groups allotted more time per problem than the Beginning Group. The average length of EPRs in the Sophisticated and Emergent Groups were relatively similar (11 min 26 s versus 9 min and 4 s, respectively), while the average length of EPRs in both of these groups was more than twice that of the EPRs in the Beginning Group (4 min 15 s). The difference in length of time spent on individual instructional problems was

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Comparing the Interactional Organization of Conceptual Resources

significantly lower in the Beginning Group than the other two groups. Specifically, the Beginning Group spent significantly less time than the Sophisticated Group, t(35)=2.96, p