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Rigorous college-and-career readiness standards require significant shifts in typical mathematics instruction. Many schools and districts employ coaches to support instructional changes. Although there is evidence that coaching programs can support teaching improvement, research has yet to identify high-leverage coaching practices. In collaboration with a network of state leaders and coaches, our research team refined a model for math coaching and documented the practices coaches employed in one-on-one work with teachers. Analysis of videotaped coaching conversations and teaching events suggests that model-trained coaches improved their capacity to use a high-leverage coaching practice--deep and specific prelesson planning conversations--and that growth in this practice predicted teaching improvement, specifically increased opportunities for students to engage in conceptual thinking.

Attempts to scale up instructional interventions confront implementation challenges that mitigate their ultimate impact on teaching and learning. In this article, we argue that learning about adaptation during the design and implementation phases of reform is critical to the development of interventions that can be implemented with integrity at scale. Through analysis of data generated during a mathematics instructional coaching initiative, we examine the adaptations coaches made to diverse relational and organizational contexts. Findings from two studies of adaptation illustrate the need to attend to the extent to which adaptations are consistent with the core features of a reform. Based on our findings, we posit a generalizable model that supports evidence-based mutual adaptation. [For the corresponding grantee submission, see ED599340.]

The past decade has witnessed a strong, standards-based call for improving what mathematics is taught and how it is taught. In the USA, districts have hired instructional coaches to help teachers shift their teaching from algorithm-based instruction to instruction that is more student-centered and conceptually focused. The purpose of this study was to contribute to the field's understanding of (a) the specific coaching practices that help teachers enact more conceptual-based forms of instruction; and (b) how coaches learn to enact those practices. Using a design-based implementation research approach, we trained coaches using a particular model for one-on-one coaching (Content-Focused Coaching); the coaches then worked with teachers to plan lessons aligned with the coaching model. Data consisted of videotapes of pre-lesson conferences that were transcribed and coded according to the model. Analyses of 32 coaches' practice over a 2-year period suggest that each of the three components of our coaching model (attention to student thinking, pedagogy, and mathematics) demonstrated statistically significant improvement over time. An illustrative analysis of five coaching sessions of one coach revealed a progression over five sessions from planning discussions that stayed at the level of general strategies to more specific conversations about teaching a particular task and then to deeper discussions that integrate attention to mathematical concepts, student thinking, and pedagogical moves. We view this delineation of coach learning as an important first step in laying the groundwork for the design of future coach training.

Teacher learning is a huge challenge in instructional change, but relatively little work has carefully examined the mechanisms by which teachers learn, in contrast to the extensive work on programs that help teachers learn and the high-leverage instructional practices that are strong predictors of student learning. Specifically, relatively little is known about how teachers learn to effectively implement these new instructional practices. Using a mixed-methods, case-comparison design, this study examines specific instructional coaching practices that support 4th-8th grade mathematics teachers in learning to implement ambitious instructional practices. The study leverages a large, state-wide representative dataset in order to purposively select carefully-matched contrasting cases for qualitative analysis from a starting sample of hundreds of teachers, which enabled selecting teachers that began in a very similar place but then progressed at different rates. In-depth qualitative coding was systematically conducted on detailed transcripts of coach-teacher conversations from these carefully selected cases. Finally, these codes were analyzed quantitatively to determine whether the content and form of these conversations predicted improvement in teachers' instructional practices. Results showed that coach-teacher pairs who discuss when and why certain practices should be implemented, and provide more opportunities for teacher input, see larger gains in ambitious instruction in later lessons. Implications for a coaching model based in the cognitive sciences are discussed.

We argue that large-scale, standards-based improvements in the teaching and learning of mathematics necessitate advances in our theories regarding how teaching affects student learning and progress in how we measure instruction. Our theory--an embodiment of the interaction of high and low levels of two constructs that past research has shown to influence students' development of conceptual understanding (explicit attention to concepts and students' opportunity to struggle)--guided the development of survey-, video-, and artifact-based measures of teaching. Here, we develop a validity argument for the inferences that can be drawn about teaching from these measures by identifying claims and empirical evidence about the extent to which those claims are born out in practice. Results suggest our theory is capturing four patterns of teaching and that it can successfully predict different types of student learning: skills efficiency measured on the state standardized test and conceptual understanding as measured through open-ended task sets.

In this article, the authors define learning goals, differentiate them from performance goals, and elaborate on their function and importance as the guiding force behind maintaining cognitive rigor during mathematics learning. Next, the authors present a framework that teachers can use to define and refine learning goals during lesson planning such that goals can become a resource during teaching. The authors infuse into this discussion snapshots from conversations between two fictitious teachers that highlight how learning goals might be constructed and refined through conversations with colleagues and enactment in classrooms.

Informed by decades of research and standards-based policies, there has been a growing demand for high-quality teaching and learning in mathematics and science classrooms. Achieving these ambitious goals will not be easy; students' opportunities for learning as shaped by the tasks they are assigned will matter the most. The purpose of this article is to revisit theory and research on tasks, a construct introduced by Walter Doyle nearly 40 years ago. The authors discuss how this construct has been used and expanded in research since then, argue for its applicability to contemporary challenges facing schools and classrooms today, and provide suggestions for future research.

A major influence on mathematics teachers' instruction is their beliefs. However, teachers' instructional practices do not always neatly align with their beliefs because of factors perceived as constraints. The purpose of this article is to introduce a new approach for examining the relationship between teachers' beliefs and practices, an approach that focuses on specific instructional practices that support the development of students' conceptual understanding and on mismatches that occur between what teachers believe to be important and what they report actually doing in the classroom. We also examine the relationship between teachers' self-reported constraints and mismatches between teachers' beliefs and practices.

Science education communities around the world have increasingly emphasized engaging students in the disciplinary practices of science as they engage in high levels of reasoning about scientific ideas. Consistently, this is a critical moment in time in the USA as it goes through a new wave of science education reform within the context of Next Generation Science Standards (NGSS). We argue that the placement of high demands on students' thinking (i.e., a high level of thinking) in combination with positioning students to use disciplinary practices as they try to make sense of scientific ideas (i.e., a deep kind of thinking) constitute critical aspects of the reform. The main purpose of this paper is to identify and describe the kinds and levels of thinking in which students engage when they are invited to think and reason as demanded by NGSS-aligned curricular tasks. Our analysis of video records of classrooms in which an NGSS-aligned, cognitively demanding task was used, revealed many ways in which the aspirational level and kind of student thinking will not be met in many science classrooms. We propose a way of characterizing and labeling the differences among these kinds and levels of thinking during the implementation of a reform-based biology curriculum. These categories, which focus on two important features emphasized in the NGSS, can help us to better understand, diagnose, and communicate issues during the implementation of high-level tasks in science classrooms.

Attaining the vision for science teaching and learning emphasized in the Framework for K-12 Science Education and the next generation science standards (NGSS) will require major shifts in teaching practices in many science classrooms. As NGSS-inspired cognitively demanding tasks begin to appear in more and more science classrooms, facilitating students' engagement in high-level thinking as they work on these tasks will become an increasingly important instructional challenge to address. This study reports findings from a video-based professional development effort (i.e., professional development [PD] that use video-clips of instruction as the main artifact of practice to support teacher learning) to support teachers' learning to select cognitively demanding tasks and to support students' learning during the enactment of these tasks in ways that are aligned with the NGSS vision. Particularly, we focused on the NGSS's charge to get students to make sense of and deeply think about scientific ideas as students try to explain phenomena. Analyses of teachers' pre- and post-PD instruction indicate that PD-participants began to adopt instructional practices associated with facilitating these kinds of student thinking in their own classrooms. The study has implications for the design of video-based professional development for science teachers who are learning to facilitate the NGSS vision in science classrooms.

There is little consensus on the kinds and amounts of teacher support needed to achieve desired student learning outcomes when mathematics is inserted into science classrooms. When supported by educative curriculum materials (ECM) and heavy investment in professional development (PD), teachers implementing a unit designed around mathematical modeling of scientific mechanisms substantially increased students' ability to make both qualitative and quantitative predictions (Schuchardt & Schunn, 2016). Because of concerns about equitable access to support resources, we investigated whether variations in PD support while retaining ECM could differentially affect two student learning outcomes: Quantitative Predictions and Qualitative Predictions. Two contrasts were performed examining: (1) the effect of reducing PD and (2) whether eliminating PD entirely caused further harm to student learning. Reducing and eliminating PD had no significant effect on student gains in Qualitative Predictions, suggesting ECM can be sufficient for teachers to support student learning of conceptual science content. However, student gains in Quantitative Predictions decreased significantly upon reducing PD; eliminating PD did not cause significant additional decreases. Combined, these findings suggest that amount of face-to face PD support necessary to achieve student-learning gains can vary depending on whether the practice requires application of qualitative science content or quantitative reasoning.

If students are to meet higher standards, all educators in the system have to learn how to engage students in reasoning about complex ideas. What levers can state boards of education and state education agencies pull to support the professional learning that makes this possible? A research-practice partnership in Tennessee may shed light on this question. This group's task was to support mathematics teachers across the state through instructional coaching. This work contributes to a body of research showing that well-designed coaching programs contribute to teacher learning and improved instruction.

Background: Recent transformative changes in science education require new learning opportunities for teachers--opportunities that include rich images of classroom enactment of the reform vision. One fruitful way for doing that is to use video clips of instruction.Teachers do not, however, learn how to improve their instructional practice from simply watching and reflecting on classroom videos. The videos need to be carefully selected and embedded in professional development in ways that--through facilitator-led, participant-centered discussion--can help teachers to notice and reason about important aspects of instruction and learning that occur in the video. Consistent with the recent efforts to identify planning and facilitation approaches that guide effective professional development (PD) programs, in this paper, we adapted the Five Practices Framework for orchestrating productive classroom discussions to describe how PD facilitators plan for and enact professional learning tasks to help science teachers learn within a video-based PD program. These practices include anticipating, sequencing, monitoring, selecting, connecting and two additional practices that set the stage for the five practices (i.e., setting goals and selecting tasks). Results: Our analyses of the video-based discussions in the PD provide insights into how the facilitators engaged teachers in video-based conversations by using the practices of monitoring, selecting, and connecting. The monitoring moves, such as clarifying, countering, and redirecting, were used by the facilitator in nearly all the PD sessions. Similarly, selecting moves were used and were consistent with the goals of the PD. Finally, analysis of facilitators' and participants' connecting comments indicated their increased capacity to make connections to the bigger ideas of teaching science by maintaining the cognitive demand on students' thinking. Conclusions: This paper provides elaborated descriptions of the five practices for planning and facilitating video-based PD and the ways in which they were enacted in a video-based PD program in science. In so doing, it proposes five practices as a guiding framework to support teachers' learning from videos. Overall, the study's results endorse the promise of a goal-driven, theory-informed design that foregrounds careful attention to teachers' thinking in ways that support their understanding of complex classroom interactions.

We investigated the alignment between a teacher survey self-report measure and classroom observation measure of ambitious mathematics instructional practice among teachers in two urban school districts using two different standards-based mathematics curricula. Survey reports suggested mild differences in teachers' instructional practices between the two districts, whereas observation ratings indicated starker differences. That said, teachers' survey and observer ratings were significantly correlated in both districts. Factors significantly predicting the extent of survey-observation alignment included teachers' grade level, Mathematical Knowledge for Teaching, cognitive demand, and--for one district--teachers' adherence to the surface-level aspects of their curriculum. Qualitative analyses suggested that teachers' survey-observation alignment could be a function of their interaction with colleagues who provided instructional models against which they could gauge the extent of their standards-based instruction. Our study has implications for research on instructional practice, as well as for school district policies to support and evaluate teachers.

Model tracing tutors represent a technology designed to mimic key elements of one-on-one human tutoring. We examine the situations in which such supportive computer technologies may devolve into mindless student work with little conceptual understanding or student development. To analyze the support of student intellectual work in the model tracing tutor case, we adapt a cognitive demand framework that has been previously applied with success to teacher-guided mathematics classrooms. This framework is then tested against think-aloud data from students using a model tracing tutor designed to teach proportional reasoning skills in the context of robotics movement planning problems. Individual tutor tasks are coded for designed level of cognitive demand and compared to students' enacted level of cognitive demand. In general, designed levels predicted how students enacted the tasks. However, just as in classrooms, student enactment was often at lower levels of demand than designed. Several contextual design features were associated with this decline. Implications for intelligent tutoring system design and research are discussed.

Many countries, including the United States, emphasize the importance of developing students' scientific habits of mind and their capacity to think deeply about scientific ideas in an integrated fashion. Recent science education policies in the United States portray a related vision of science teaching and learning that is meant to guide the improvement efforts of science teachers, professional developers, and school leaders, as well as the design efforts of curriculum and assessment developers. To understand the extent to which this vision is being enacted in science classrooms, we consider the tasks to which students are exposed as representative of the types of opportunities that they have to think, reason, and engage in disciplinary ideas and practices in science classrooms. The purpose of this article is to advance a framework to analyze science tasks and instruction in terms of two dimensions that are critical for science learning: (1) cognitive demand; and (2) the integration of scientific content and practices. We present the Task Analysis Guide in Science (TAGS) framework through a detailed description of its categories along with concrete examples of science tasks in each category. We compare it to other frameworks related to cognitive demand. We conclude by discussing various ways in which the TAGS can serve as a helpful analytical tool for educational researchers and practitioners.

This study sought to understand the opportunities and challenges associated with the implementation of state designed Race to the Top (RttT) funded reform networks. Drawing on a conceptual framework developed from the networked governance literature, we analyzed the 12 state RttT grantees' applications. Our analysis revealed that states designed large implementation networks with potential to bring a wide range of resources to bear on reform efforts, particularly through participation of numerous nonsystem actors. However, coordinating large and diverse networks places state education agencies (SEAs) in a new and challenging role. The extent to which networks extend state capacity to support educational improvement or further complicate the work of SEAs remains an open question. We propose a model including a set of theoretical propositions to guide future research.

Students' opportunities to learn how to think are embedded in the instructional tasks with which they are invited to engage in the classroom. Prior research has revealed that the selection and use of cognitively demanding tasks does not guarantee high-level student thinking during their enactment. To address this challenge, we designed and implemented a professional development (PD) in which participants analyzed video clips of the enactment of cognitively demanding science tasks. Using transcripts of pre-and post-PD interviews during which participants were asked to respond to specially selected video clips, we analyzed what the participants attended to and how they made sense of what they saw. The findings suggested a change in terms of a growing tendency to attend to teaching as constituted in the interaction of the teacher, students, and task and to adopt an interpretive stance while talking about what was seen in the video clip.

This article examines how a coding scheme for mathematics classroom discussion that was created to highlight how teachers negotiate student responses during whole-class discussion around high-level, cognitively demanding tasks was used to help teachers shift what they notice when analyzing classroom discourse. Data from an intervention that trained teachers how to use the coding scheme and then provided them opportunities to use the scheme to code transcripts of classroom discussion are presented. Results suggest that teachers' ability to notice interactions between teacher and students when analyzing classroom discussion (as opposed to focusing on one actor or the other) can be increased and that teachers can learn to identify specific discourse moves teachers use to negotiate student responses. However, teachers' capacity to identify how students' opportunities to learn are related to teacher discourse moves did not change as a result of the intervention. The article goes on to examine how discussion during the intervention itself may have contributed to what teachers learned to notice. This research contributes to the body of work on teachers' noticing by examining the feasibility and efficacy of using transcripts and a coding scheme to foster teachers' ability to notice how they can increase their students' opportunities to learn through mathematics discourse.

The authors review what is known about early and universal algebra, including who is getting access to algebra and student outcomes associated with algebra course taking in general and specifically with universal algebra policies. The findings indicate that increasing numbers of students, some of whom are underprepared, are taking algebra earlier. At the same time, other students with requisite skills are not given access to algebra. Although studies using nationally representative data indicate strong positive outcomes for students who take algebra early, studies conducted only in contexts where all students are mandated to take algebra in eighth or ninth grade provide mixed evidence of positive outcomes, with increased achievement when policies include strong supports for struggling students. The authors conclude with a call for studies that examine the relationship among algebra policies, instruction, and student outcomes to understand the mechanisms by which policies can lead to success for all students. (Contains 9 notes and 6 tables.)

This article begins to unravel the question, "What curricular materials work best under what kinds of conditions?" The authors address this question from the point of view of teachers and their ability to implement mathematics curricula that place varying demands and provide varying levels of support for their learning. Specifically, the authors focus on how teacher capacity (their level of education, experience, and knowledge) and their use of curriculum influence instruction. The study sample is 48 teachers implementing two standards-based mathematics curricula--"Everyday Mathematics" and "Investigations"--in two school districts. The data include interviews and surveys with teachers, as well as observations of instruction, over a 2-year period. Findings indicate that teachers' implementation of "Investigations" was considerably better than teachers' implementation of "Everyday Mathematics" in terms of maintaining high levels of cognitive demand, attention to student thinking, and mathematical reasoning. These implementation measures were not correlated to measures of teacher capacity across school districts. However, implementation measures were significantly correlated with teachers' lesson preparation that took into account the big mathematical ideas within curriculum. Further qualitative analysis indicated that the "Investigations" curriculum provided more support to teachers for locating and understanding the big mathematical ideas within lessons compared to "Everyday Mathematics". (Contains 6 tables, 1 figure and 11 notes.)

We bring together education research on factors shaping teacher learning with institutional research on policy shifts and conflicts to explore an instructional policy shift in one school district. Specifically, we compare mathematics teacher learning opportunities in three elementary schools over a three-year period during which a district policy shift toward English as a Second Language (ESL) instruction diverted attention from mathematics curriculum reform efforts. Findings demonstrate that while the policy shift led to significant decreases in mathematics teacher learning opportunities across the district and in two of the case study schools, mathematics teacher learning opportunities were sustained in one case study school due to two school-level strategies: a common, articulated vision for mathematics instruction and a high number of mathematics-focused teachers in the school. Together, these two strategies supported the creation of coherence between mathematics and ESL policies in the school, which encouraged the maintenance of mathematics teacher learning opportunities. (Contains 7 notes and 5 tables.)

Teachers who attempt to use inquiry-based, student-centered instructional tasks face challenges that go beyond identifying well-designed tasks and setting them up appropriately in the classroom. Because solution paths are usually not specified for these kinds of tasks, students tend to approach them in unique and sometimes unanticipated ways. Teachers must not only strive to understand how students are making sense of the task but also begin to align students' disparate ideas and approaches with canonical understandings about the nature of mathematics. Research suggests that this is difficult for most teachers (Ball, 1993, 2001; Leinhardt & Steele, 2005; Schoenfeld, 1998; Sherin, 2002). In this article, we present a pedagogical model that specifies five key practices teachers can learn to use student responses to such tasks more effectively in discussions: anticipating, monitoring, selecting, sequencing, and making connections between student responses. We first define each practice, showing how a typical discussion based on a cognitively challenging task could be improved through their use. We then explain how the five practices embody current theory about how to support students' productive disciplinary engagement. Finally, we close by discussing how these practices can make discussion-based pedagogy manageable for more teachers. (Contains 2 figures, 1 table, and 2 notes.)

This article explores the usefulness of communities of practice theory for understanding how districts can create organizational environments that foster teachers' opportunities to learn the new ideas and practices required to carry out ambitious reforms. It draws on data from a longitudinal study of the implementation of ambitious mathematics curricula in two urban districts. By analyzing the contrasting ways that teachers in two schools in each district were linked to each other and reform efforts at the district level, the article shows how the district reform effort in one district led to significant opportunities for teacher learning and alignment with reform goals while efforts in the other district coordinated action but failed to spur meaningful opportunities for teacher learning. The article closes with implications for policy and practice. (Contains 2 figures, 1 table and 22 notes.)

Examined one New York City school district's literacy improvement efforts. Data from document reviews, interviews, and observations highlighted strong parallels between how children learned to read and how teachers learned to teach. These parallels stemmed from the way the professional development system was anchored on the Balanced Literacy Program and from the district's belief in authentic and social learning. (SM)

Describes a study on how effective teachers use manipulatives successfully. Presents factors to recognize when manipulative-based lessons are identified and discusses ways in which the use of manipulatives can go astray. (YDS)