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Despite the complexity of facilitating professional development (PD) and growing attention to supporting facilitators, few tools exist for facilitators to engage in ongoing inquiry into their practice. In this article, we offer a practical measure, the Collaborative Professional Development Survey (CPDS), designed to provide facilitators with information about teachers' perceptions of aspects of the PD learning environment that research indicates matter for teachers' opportunities to learn. We illustrate how facilitators used the CPDS to support their collective inquiry into facilitation. We also illustrate the social processes that appeared to enable facilitators' productive use of the CPDS, including a routine to analyze the resulting data, and the orientations that underpinned their analysis. We discuss implications for facilitators' use of the CPDS.

Supporting teacher learning for normative change in classroom learning environments creates significant demands on principal leadership. We offer an analytic framework that aims to understand principal practice for instructional transformation. The framework examines how the principal's conception of teacher learning shapes practice in relation to particular contexts and support systems. We illustrate the explanatory power of this framework by using it to make sense of one elementary principal's practice in leading her school for instructional transformation in mathematics. Our analysis contributes to how leadership efforts to transform instruction might be studied and ultimately supported.

Recent innovations in professional development are rife with a wide array of efforts focused on teacher collaboration. In this essay, we address some of the unexamined assumptions about the nature and significance of interactions in teacher professional collaboration, drawing on the concept of the "fourth wall" from theater and film studies. The "fourth wall" is a term used to describe the invisible wall that separates actors from their audience. We use this metaphor to interrogate the function of the fourth wall in professional learning and argue that it reflects a culture of professional learning that, despite innovations that tout teacher collaboration, upholds isolation in teaching and teacher learning and deep embedded norms of noninterference in one another's practice. We also attend to the possibilities for supporting teacher learning that breaching the fourth wall affords when shared enactments of practice are used as a context for teachers' sensemaking and collaboration.

This analysis examines the process of one research-practice partnership (RPP) engaged in the activity of decomposing elementary principal practice in the context of an instructional improvement initiative in mathematics. Decomposing, or breaking apart, complex practice has been used primarily by researchers to inform the design of pre-service teacher education. We argue that decomposition is a rich activity for researchers and practitioners to collaboratively engage in to support improvement efforts where practitioners are expected to transform their day-to-day practice. We examine what can be learned from the process by which one RPP engaged in decomposing practice that might be useful for other RPPs. Our retrospective, qualitative analysis supports understanding of how RPPs might engage in decomposition and the role decomposition might play in supporting RPPs to foster educational transformation in local contexts.

Researcher-practitioner collaborations often stop short of engaging researchers and teachers in collectively negotiating the moment-to-moment improvizational decision-making of instructional practice when students are present. We consider the potential for learning at one boundary that often exists between researchers and practitioners as they collaborate on instructional practice: the boundary between performing-teaching and observing-teaching. We draw on performance studies to conceptualize this boundary as a fourth wall. Our analysis examines researcher-practitioner collaboration across four sites in which participants were learning together about the complex work of facilitating student discussion. We analyze how one boundary crossing routine provided opportunities for researchers and practitioners to interact at the boundary of the fourth wall during enactment of discussion-based instruction with students. To analyze episodes of this routine, we draw on conceptualizations of potential learning mechanisms of boundary crossing in research-practice partnerships. Our findings identify and describe the mechanisms for researcher/practitioner learning that arose when our participants crossed the boundary of the fourth wall: perspective taking, boundary spanning, and recognition of shared problem spaces. We argue that these learning mechanisms create potential for researchers and practitioners to wrestle with and learn about the challenges and opportunities within facilitation of student discussions.

Engaging students in mathematical argumentation supports language development and conceptual understanding because students use verbal and written language in coordination with mathematical representations to notice patterns, make claims, and create and revise explanations. This study adds to the limited research base on how teachers learn to facilitate discussions specifically aimed to develop students' capacities to engage in argumentation. We analyze teachers' sensemaking about supporting argumentation in the classroom through their participation in an adaptive professional development (PD) design. The PD was embedded in two elementary schools with upper grade teachers which enabled them to engage in iterative cycles of investigation and enactment within their own classrooms. Through collaborative lesson design and inquiry into students' experiences, teachers attended to the language students produced as they tried to formulate conjectures and produce explanations and the classroom participation structures that supported them. Our results suggest shifts in how teachers understood their role. Both cases speak to the complexities teachers face as they try to realize the recommendations for enhancing language learning and provide insight into what "rich" discourse means.

Supporting prospective teachers to enact high quality instruction requires transforming their methods preparation. This study follows three teachers through a practice-based elementary methods course. Weekly class sessions took place in an elementary school. The setting afforded opportunities for prospective teachers to engage in cycles of investigation and enactment. The course was focused on learning teaching practices through planning, rehearsing, enacting and reflecting on routine instructional activities that travel back and forth between field-based methods course and field placements. All three teachers grew in their capacity to lead goal-directed lessons by eliciting and responding to students' thinking. Our analysis connects the teachers' learning to the intentional design of the methods course.

The promise of university-public school partnerships as contexts for mutually beneficial learning, or "simultaneous renewal," has been well established (Goodlad, 1994, 1999). However, difficulties in creating and sustaining these kinds of collaborative contexts for teacher education are also well known, including practical challenges such as time and distance, as well as the nuanced and layered tensions between institutional missions, cultures, and practices (Mantle-Bromley, 2002; Teitel, 1997). Contemporary efforts to create and sustain university-public school partnerships are further complicated by dramatically increased accountability pressures arising from No Child Left Behind (NCLB). Discretionary time for public educators is a scarce and dwindling resource. As high stakes testing and related accountability pressures increase on institutions of higher education, chronic shortages of resources to support collaborative work with public school partners are a widely acknowledged fact of life in partnership work. In the context of these kinds of institutional pressures it is clear that collaborative partnership work must be carefully designed to yield visible and valued benefits for both university and public school-based educators (Yendol-Hoppey, League, Gregory, Ohlson, & Jackson, 2006). In this article, the authors describe a design strategy aimed at creating shared opportunities for teacher learning and development, including the learning of university faculty, that may be embedded in practical activities related to the analysis of P-12 student work. The authors offer three illustrations of how they have used this strategy to design shared contexts for learning that are relevant to the (differing) needs of teacher candidates, public school colleagues and university faculty. (Contains 1 table and 1 figure.)

Background/Context: The literature review by Phelps in this special issue highlights the challenges of research-practice partnerships and other forms of insider-outsider collaboration in education. In addition to addressing well-known challenges, this case study article focuses on the full-service community school model as a strategy to address holistic needs of students, families, and staff in poverty-impacted school contexts. Purpose/Objective/Research Question/Focus of Study: This article documents work that was conducted across five years, when a large research university partnered with an urban elementary school to establish a full-service community school. It provides an account of the assets, challenges, and processes that impacted our work, from the planning phase through four years of implementation. It describes efforts around four main areas: academic excellence, extended learning, holistic health and wellness, and family engagement. Research Design: This is a participatory case study with university educators and researchers working collaboratively with school professionals, community-based organizations, and families. Data Collection and Analysis: Many sources of data were included in our case analysis, including formative and summative student assessments, student attendance, service referrals, and office referrals for behavior. Running records of meetings, documentation of events, presentations, and reports submitted were also included. Interviews with key actors in the project were also collected and analyzed. Conclusions/Recommendations: Our partnership experienced some of the major challenges discussed in the literature. Turnover was overwhelmingly the most significant challenge. Student mobility and district boundary changes, new curricular adoptions for mathematics and literacy, new student assessments, new data tracking system, new bell times, and measures to cut transportation costs also impacted the effort. In spite of these challenges, we also experienced important successes. Centering relationships in our work has been an essential part of the success we experienced and is itself a success. At every phase, we remained at the table together, working to build relationships and sharing visions, goals, and practices. This resulted in important changes with stronger systems for tracking and using student data in educational decision making, health and wellness services now available to all students, and a universal social-emotional curriculum now in place. Family engagement and parent leadership are now essential dimensions of the school, with parents of color playing important roles to amplify their own and other parents' voices. Preservice teachers learned about full-service community schools in situ. We highlight the rich and complex narrative that emerged, which is not simply one of challenge but also one of resilience and strength. Carefully documenting this initiative can contribute to guiding implementation and refinement of a full-service community school model.

A core function of district leadership is providing instructional vision and support for school leaders and teachers. In this article, a Research-Practice Partnership focused on the improvement of elementary mathematics teaching and learning provides the context to study leadership development. We examine the process of one design team within the Research-Practice Partnership consisting of district leaders and university researchers using organizational learning. We found that as the team iteratively negotiated the design and implementation of a practical measure aimed at assessing and improving elementary mathematics instruction system-wide, the team's learning transformed the tools and routines of its work.

In this response to Kalenic-Craig's (2017) article, "The Rights of the Learner: A Framework For Promoting Equity through Dynamic Formative Assessment," I consider what implications the RotL framework has for the work that teachers and students must do in learning environments where these rights flourish. The RoTL emphasizes student sensemaking and communication in the classroom. Given the realities of classrooms as racialized, gendered, and classed spaces, this emphasis on communication demands critical consciousness for both teachers and students. [For "The Rights of the Learner: A Framework for Promoting Equity through Formative Assessment in Mathematics Education," see EJ1162636.]

In this article, we report on "Researching Mathematics Leader Learning" ("RMLL"), a project designed to support leaders in learning how to facilitate robust opportunities for teachers' mathematical learning. Our two-phase research design allowed us to construct a set of videocase seminars, enact the seminar design with leaders, analyze these data, refine our seminar design, and implement a second set of seminars with a new group of leaders. We drew on the noticing literature to examine leaders' pedagogical reasoning as they discussed videocases of professional development. In this article, we demonstrate how changes in our framework for leader development and the resulting changes in the prompts and tasks shaped leader noticing in three ways: (a) accounting for the mathematical work of the facilitator and teachers in the videocase; (b) linking the mathematical work to goals for teacher learning; and (c) reasoning around the facilitator's work in advancing those learning goals. Analysis indicates that in Phase II, leader discussions were more focused on the mathematical and pedagogical work needed to advance teacher learning. Based on our research and development work with over 70 leaders, we offer a set of design principles for leader professional development.

The goals of problem-solving activities in the elementary grades often include making sense of story problems, developing a range of strategies, and reaching accurate solutions. These are important mathematical aims, but they do not fully address the demands of modeling with mathematics as described in the fourth of the Common Core's eight Standards for Mathematical Practice (SMP 4) (CCSSI 2010, pp. 6-8). Modeling with mathematics also involves identifying mathematical problems in the world, gathering information and determining which details will help solve a problem, and developing and revising mathematical models of situations. For young children, such models might include diagrams, equations, and using manipulatives to represent the quantities and mathematical relationships in a given situation. After investigating various approaches and activities, this group of teachers, coaches, and teacher educators from various school settings in the Seattle area discovered an exciting problem solving activity structure specifically designed to engage students in mathematical modeling: Three-Act Tasks (Meyer 2011) designed by Dan Meyer for use in secondary classrooms and adapted by Graham Fletcher and other educators for elementary school classrooms (Fletcher 2016). The activity structure comprises three parts or "acts." This article provides a summary of a three-act lesson. Originally designed for secondary mathematics students, this group of educators found the three act approach to be productive for even the youngest learners and invites readers to tap into elementary students' intuitive ability to make sense of problems in a new way that presents entry points for all learners.

Eliciting, responding to, and advancing students' mathematical thinking all lie at the heart of great teaching. In this article, the authors describe a formative assessment approach that teachers can use to learn more about their students' mathematical thinking and inform their instructional decisions. This assessment approach draws on a widely known set of frameworks for children's thinking, Cognitively Guided Instruction (CGI) (Carpenter et al. 2014). It enables teachers to learn from students by giving them time to voice their understandings and confusions. By listening carefully, teachers convey to students that their experience matters. The primary purpose of assessment is to inform and improve the teaching and learning of mathematics. The assessment approach described in this article gives teachers opportunities to talk with students about their mathematical thinking and gain a better understanding of their students as mathematicians.

In recent years, work in practice-based teacher education has focused on identifying and elaborating how teacher educators (TEs) use pedagogies of enactment to learn in and from practice. However, research on these pedagogies is still in its early development. Building on prior analyses, this article elaborates a particular pedagogy of enactment, "rehearsal", developed through a collaboration of elementary mathematics TEs across three institutions. Rehearsals are embedded within learning cycles that provide repeated opportunities for novice teachers (NTs) to investigate, reflect on, and enact teaching through coached feedback. This article shares a set of insights gained from 5 years of developing, studying, and learning how to support NTs' enactment in rehearsal. The insights we share in this article contribute to building a knowledge base for pedagogies of teacher education.

Supporting students to develop an understanding of the meaning of fractions is an important goal of elementary school mathematics. This involves developing partitioning strategies, creating representations, naming fractional quantities, and using symbolic notation. This article describes how teachers can use a formative assessment problem to elicit and understand students' ideas about the meaning of fractions. The fraction problem described in this article was designed using research on children's thinking in elementary mathematics, and it enables teachers to uncover students' understanding of the following essential aspects of understanding the meaning of fractions: (1) partitioning strategies; (2) representations; and (3) language and notation.

By simply asking students how they got the answer to a problem, math teachers can open the door to stimulating discussions in class. But how can they make sure those discussions promote mathematical understanding? Allison Hintz and Elham Kazemi explain that teachers need to know what the goal is for a discussion and plan accordingly. The authors discuss to kinds of math discussions: open strategy sharing and target sharing. Open sharing is the best technique to use when teachers want students to become aware of different ways to solve a problem. Targeted sharing is better when teachers want students to make sense of particular strategies. For example, a 4th grade teacher could have students share their answers to the problem 24 divided by 4 and explain how they got that answer. A follow-up discussion could compare two different ways students solved the problem and what those methods tell them about division. In all types of mathematical discussion, it's important that teachers treat students as mathematical thinkers, giving them opportunities to share, recording their responses, and allowing them to revise their responses as their understanding develops.

In this article, we argue that teaching is and should be a central element to learning to teach, particularly as teacher education once again turns toward practice. From this perspective, we must elaborate how such a shift addresses the need to bridge the gap between knowledge for teaching and knowledge from teaching, between theory and practice, and among university courses and fieldwork. If the intent of such a shift is to fundamentally change the preparation of teachers, we argue that it requires teacher education programs to do more than increase the amount of time candidates spend in clinical field placements. It requires, we argue, that teacher educators engage in simultaneous innovation in three related, but distinct aspects of program design and implementation: organizational structures and policies, content and curriculum, and teacher education pedagogy. Without such dynamic engagement, the practice-turn will go the way of many past reforms in teacher education--it will be symbolic but not significant or meaningful.

We analyze a particular pedagogy for learning to interact productively with students and subject matter, which we call “rehearsal.” Our goal is to specify a way in which teacher educators (TEs) and novice teachers (NTs) can interact around teaching that is both embedded in practice and amenable to analysis. We address two main research questions: (a) What do TEs and NTs do together during the kind of rehearsals we have developed to prepare novices for the complex, interactive work of teaching? and (b) Where, in what they do, are there opportunities for NTs to learn to enact the principles, practices, and knowledge entailed in ambitious teaching? We detail what happens in rehearsals using quantitative and qualitative methods. We begin with the results of our quantitative analyses to characterize how typical rehearsals were structured and what was worked on. We then show how NTs and TEs worked together to enable novices to study principled practice through qualitative analyses of a particularly salient aspect of ambitious teaching, namely, eliciting and responding to students' performance. (Contains 3 tables, 2 figures, and 5 notes.)

Currently, the field of teacher education is undergoing a major shift--a turn away from a predominant focus on specifying the necessary knowledge for teaching toward specifying teaching practices that entail knowledge and doing. In this article, the authors suggest that current work on K-12 core teaching practices has the potential to shift teacher education toward the practice of teaching. However, the authors argue that to realize this vision we must reimagine not only the curriculum for learning to teach but also the pedagogy of teacher education. We present one example of what we mean by reimagined teacher education pedagogy by offering a framework through which to conceptualize the preparation of teachers organized around core practices. From our perspectives, this framework could be the backbone of a larger research and development agenda aimed at engaging teachers and teacher educators in systematic knowledge generation regarding ambitious teaching and teacher education pedagogy. We conclude with an invitation to the field to join with us in imagining approaches to generating and aggregating knowledge about teaching and the pedagogy of teacher education that will move not only our individual practice but also our collective practice forward.

Filling the knowledge gap in the limited research on professional development leaders is an urgent issue if teacher learning is to be improved. This research and development project is studying how leaders learn to cultivate mathematically rich professional development environments. The authors adapted two frameworks from classroom-based research--sociomathematical norms and practices for orchestrating productive discussion--to support leaders' understanding of facilitation of mathematics professional development. In this article, the authors describe the use of these frameworks in their work and argue for a third framework--the mathematical knowledge for teaching. Based on the analysis of their work, they believe that mathematics professional development leaders need to cultivate particular sociomathematical norms for teacher explanation and employ practices for orchestrating discussions to achieve the purposeful development of teachers' specialized knowledge of mathematics for teaching. (Contains 1 table and 8 notes.)

Research on professional development (PD) typically focuses on what teachers learn as a result of their participation in PD. Questions are framed unidirectionally: To what extent does participation in PD affect teachers' classroom practice? The authors challenge this unidirectional conceptualization of teacher learning and instead argue for understanding the multidirectional influences between teachers' participation across the PD and classroom settings. Drawing on research in mathematics education, they argue that researchers should examine what teachers are learning during and after PD, looking at the "coevolution" of participation between classroom practice and PD. To advance studies of and designs for PD, the authors' perspective leads them to argue for the importance of better understanding how teachers come to make sense of primary artifacts, depictions, and enactments in and through PD. (Contains 6 notes and 1 table.)

Although most educators would agree that enacting cultural relevance in the classroom is always a complex process, we have too few examples in the research literature of what that complexity looks like and how it plays out in highly diverse classrooms. Drawing on a range of qualitative data sources, this case study examines how one teacher's interpretation of culturally relevant pedagogy bumped up against children's ideas about their own and others' cultural and racial positionings in an elementary classroom where both cultural background and race varied. The authors argue that it is vital for teachers and researchers to consider cases such as this if we are to better understand and respond to the complexities of substantively engaging children in issues of culture and race in diverse public school communities. (Contains 1 table.)

This article presents a case study of a fourth grade boy's experiences in writing, preceding and following a story he wrote about a boy whose struggles in writing led directly to his death. We explore how Max's writing experiences related to his identity, specifically his sense of himself as a writer, his struggle to communicate his ideas, and his discomfort with expressing private thoughts and emotions in print. Drawing on a range of qualitative data, we examine Max's experiences with writing workshop, journal writing, responding to literature, and a state writing assessment. Max's story argues for the importance of considering issues of identity in the writing classroom to help students build on the successes that often hide behind the surface struggles of their writing. (Contains 4 figures and 1 table.)

This article discusses children's experiences with a literacy project intended to celebrate the cultures represented in a highly diverse fourth/fifth grade urban elementary classroom. However, when other children questioned the claimed identities of three biracial children, the project was transformed from a rather straightforward attempt to acknowledge and honor diversity into a critical literacy project in which children grappled with the complexities of race and what it means to claim membership in racial categories. (Contains 1 figure.)

The study describes teachers' collective work in which they developed deeper understanding of their own students' mathematical thinking. Teachers at one school met in monthly workgroups throughout the year. Prior to each workgroup, they posed a similar mathematical problem to their students. The workgroup discussions centered on the student work those problems generated. This study draws on a "transformation of participation" perspective to address the questions: What do teachers learn through collective examination of student work? How is teacher learning evident in shifts in participation in discussions centered on student work? The analyses account for the learning of the group by documenting key shifts in teachers' participation across the year. The first shift in participation occurred when teachers as a group learned to attend to the details of children's thinking. A second shift in participation occurred as teachers began to develop possible instructional trajectories in mathematics. We focus our discussion on the significance of the use of student work and a transformation of participation view in analyzing the learning trajectory of teachers as a group.

Examines ways in which classroom practices create a press for conceptual mathematical thinking and how teachers can promote student participation in a classroom community where conceptual understandings are valued and developed. Details four important sociomathematical norms characterizing a high press for conceptual thinking. Concludes that a high press for conceptual thinking allows the mathematics to drive student engagement in activities. (Author/SD)

Describes a research and development project, Cognitively Guided Instruction, to illustrate how theory and research inform the teaching and learning of mathematics. The project engaged first grade teachers with research-based knowledge about the development of children's mathematical thinking, studying teachers' use of this knowledge in the classroom and examining changes in their beliefs and knowledge. (SM)