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A major affordance of one-on-one mathematics coaching is its potential to provide individualized, contextualized support for mathematics teachers' learning. Coaches can adjust their work to individual teachers by focusing on instructional improvement goals that take account of teachers' current knowledge, practice, and classroom contexts. It is, however, essential that coaches and teachers work to attain productive instructional improvement goals that are both feasible for teachers to attain and likely to result in immediate improvements in students' learning, if attained. In this article, we describe how coaches can identify productive goals for individual teachers and then, on that basis, negotiate goals successfully with teachers, thereby supporting teachers in seeing productive goals as worthwhile. By describing these two processes, we further clarify the forms of coaching-specific expertise central to effective one-on-one mathematics coaching.

This study aims to compare teachers' self-efficacy across Turkish and American in-service middle-school mathematics teachers. The samples consist of 379 Turkish and 245 American in-service middle-school mathematics teachers. The self-efficacy questionnaire of the Middle-school Mathematics and the Institutional Setting of Teaching (MIST) scale was used in the study. The exploratory factor analysis revealed two dimensions of the self-efficacy measures across the American and Turkish teachers, such as classroom management and student support strategies. The measurement invariance property of the scale was evaluated before comparing the means of the groups. Despite the differences between the education systems, teachers' efficacy beliefs function quite similarly across the countries. The statistically significant mean differences in the subscale scores of efficacy measures between Turkish and American samples have no practical value. In both countries, teachers reported high level of confidence in efficacy beliefs in classroom management and student support strategies.

Instructional improvement initiatives in many districts include instructional coaching as a primary form of job-embedded support for teachers. However, the coaching literature provides little guidance about what activities coaches should engage in with teachers to improve instruction. When researchers do propose activities, they rarely justify why those activities might support teacher learning. Drawing on the preservice and inservice teacher education literatures, we present a conceptual analysis of learning activities that have the potential to support mathematics and science teachers to improve practice. We argue that our analysis can inform research on mathematics and science coaching, coaching policies, and the design of professional learning for coaches.

Supporting students' engagement in meaningful mathematics discussions can be challenging. It involves, for example, choosing tasks that are worth discussing (e.g., Stein and Lane 1996), negotiating norms for how students engage with one another's ideas (Kazemi and Stipek 2001; Horn 2012), eliciting students' thinking, and pressing students to explain their reasoning in ways that other students can understand (Cobb 1998; Thompson et al. 1994). As such, improving the quality of mathematics discussions is not an easy task and requires ongoing support in planning for and leading discussions as well as analyzing whether students learned through discussions and how teachers' instructional decisions contributed to that learning (Kazemi and Hintz 2014; Smith and Stein 2018). In this article, the authors describe a set of surveys that collect information about students' experiences of small-group and whole-class discussions and that can inform planning for and subsequent analysis of discussions, especially in professional learning settings (e.g., coaching, professional learning communities). First they describe how the survey items provide information about key aspects of discussions that shape students' opportunities to learn. Then they share two cases that highlight how teachers and instructional leaders can use the surveys in professional learning settings to identify and work toward shared goals for improving classroom discussions.

In this article, the authors present an analysis of two views of culture reflected in equity scholarship and their implications on research and mathematics teaching. In doing so, they draw on two interrelated theoretical orientations to describe instructional practices that support equitable learning opportunities in mathematics classrooms. These two orientations are grounded in contrasting views of culture. They discuss the contributions of and the tensions associated with each orientation, and argue for a research agenda that focuses primarily on what is called the Cultural Participation Orientation. In addition, the authors discuss the usefulness of drawing on both orientations in understanding equitable instructional practices in urban mathematics classrooms.

Principals and instructional coaches are asked to organize their schools to support teachers' ongoing professional learning. Prior studies have examined what principals do to support coaches rather than the ways they work together to support instructional improvement. We build on prior studies by examining how principals and coaches coordinate their work to support instructional improvement. To examine coordination, we selected cases in which coaches were or were not successful in interacting with teachers around teaching mathematics. We then analyzed the data within and across each of four cases. In schools where coaches were identified as successful in interacting with teachers, principals and coaches coordinated their work across three settings in order to jointly support teachers: teacher collaborative meetings, classroom visits, and coach-principal informal meetings. This study contributes to the literature on leadership by specifying how principals and coaches can coordinate their individual and collective work to organize supports for teachers.

We report on five-year professional development collaboration with a group of middle-school mathematics teachers during which their views of what constitutes a productive classroom statistical activity changed. The teachers' statistics instruction was initially typical in the US context and focused on producing calculations and following conventions for making graphs. In contrast, towards the end of the collaboration, teachers routinely planned statistical activities in which the generation and analysis of data was driven by a need to gain insight into a specific problem at hand. We document the changes in teachers' views of a productive classroom statistical activity and the means by which these changes were supported. In doing so, we highlight how explorations of the role of problem context in statistics provided a productive professional development focus, where teachers both built on their existing practices, and tested, in their classrooms, ideas that were novel or incongruent with their prior experiences.

Our purpose in this article is to propose a comprehensive, empirically grounded theory of action for improving the quality of mathematics teaching at scale. In doing so, we summarise current research findings that can inform efforts to improve the quality of mathematics instruction on a large scale, and identify questions that are yet to be addressed. We draw on an ongoing collaboration with mathematics teachers, school leaders, and district leaders in four urban school districts in the US. The provisional theory of action that we report encompasses a coherent system of supports for ambitious instruction that includes both formal and job-embedded teacher professional development, teacher networks, mathematics coaches' practices in providing job-embedded support for teachers' learning, school leaders' practices as instructional leaders in mathematics, and district leaders' practices in supporting the development of school-level capacity for instructional improvement. (Contains 1 footnote.)

Purpose: This study examines the content and efficacy of instructional leaders' expectations and feedback (press) in relation to the improvement of middle school mathematics teachers' instruction in the context of coherent systems of supports. Research Method/Approach: This mixed methods study is a part of a larger, 8-year longitudinal study in four large urban school districts across the United States. We used transcripts of interview data, surveys, and video recordings of instruction of 271 cases, over 4 years, to determine the content of administrator press, as reported by teachers, and the relationship between the content and change (if any) in instruction. To do so we used qualitative coding of interview transcripts, and ran a series of statistical models to examine the nature of the variance in and impact of administrative press. Findings: Most of the administrators' press, as reported by teachers, was not targeted toward specific teachers' mathematics instruction in ways that would likely lead toward improvement in those practices. Rather, the press focused on content-neutral instructional practices or classroom management and organization. Implications for Research and Practice: The instructional leadership practice of administrator observation and feedback is widespread, yet understudied as it relates to changes in teacher practice. Our findings indicate that current policies that mandate principals to spend substantial time in classrooms are unlikely to result in significant improvements in the quality of instruction unless meaningful resources are invested to support administrator learning.

Many districts are using content-focused coaching as a strategy to provide job-embedded support to teachers. However, the current coaching literature provides little guidance on what coaches need to know and be able to do to engage teachers in activities that will support their development of ambitious instructional practices. Furthermore, little is known about how and why effective coaches choose to design particular types of activities with certain teachers. In this article, we report an exploratory case study that examined a mathematics coach who consistently engaged teachers in coaching activities that had the potential to support their development when she worked with them one-on-one in their classrooms. In presenting an analysis of the coach's design of coaching activities, we describe five aspects of her planning practice and delineate the knowledge implicated in those practices. The findings clarify goals for coaches' professional learning, and therefore have implications for school and district coaching policies.

District leaders often feel that working with researchers is not mutually beneficial. Researchers do not provide enough practical guidance, and they are often unable to present their findings in time to inform district decision making. Research-practice partnerships (RPPs) are a potential new strategy for addressing these challenges. RPPs are long-term, mutual collaborations between practitioners and researchers that are organized to investigate problems of practice and solutions for improving district outcomes. By focusing on real-time district challenges, RPPs can lead to research that is informative, timely, and relevant to district stakeholders.

We examined the extent to which mathematics program evaluations that have been conducted according to methodologically rigorous standards have attended to the theories underlying the programs being evaluated. Our analysis focused on the 37 reports of K-12 mathematics program evaluations in the last two decades that have met standards for inclusion in What Works Clearinghouse syntheses. Each report was coded for the extent to which program theory was articulated and used in the evaluation, and for evaluator, study, and program characteristics. Our analyses revealed that very few evaluations attended to program theory, but that aspects of program theory use--as well as reported effect sizes--varied by study and evaluator characteristics.

The importance of teachers developing adaptive instructional practices consistent with metaphor of whole-class scaffolding has been well documented. However, teachers' development of such practices is currently not well understood. We draw on a 5-year professional development (PD) design experiment in which a group of middle school mathematics teachers developed aspects of such practices. We address questions of "how can teachers' development of instructional practices consistent with whole-class scaffolding be supported", and "what challenges should be anticipated when designing to support such development?" Findings indicate that leveraging teachers' existing practices and concerns was important in supporting them to focus on students' mathematical reasoning and develop adaptive practices. We discuss how the notion of whole-class scaffolding can orient the design of PD activities that remain grounded in classroom practice, and also consider how this notion can be further refined through analyses of teachers' learning in PD settings.

In this paper, we frame the dissemination of the products of classroom design studies as a process of supporting the learning of large numbers of teachers. We argue that high-quality pull-out professional development is essential but not sufficient, and go on to consider teacher collaboration and one-on-one coaching in the classroom as additional supports. We then illustrate that it is also important to identify other aspects of the school context that need to be addressed by a dissemination design, such as school instructional leadership and teachers' access to colleagues who have already developed relatively accomplished instructional practices. We conclude by discussing how researchers who conduct classroom design studies can make the challenges of dissemination more tractable by designing with an eye towards large-scale implementation. Our suggestions include that they make the design study teacher's relatively sophisticated instructional practices an explicit focus of analysis and that they assess whether it is realistic to expect teachers to learn to enact the products of the study effectively given their current instructional practices and the capacity of educational systems to support their learning.

A key aspect of supporting teachers' learning on a large scale concerns mathematics leaders' practices in designing for and leading high-quality professional development. We report on a retrospective analysis of an initial design experiment aimed at supporting the learning of three math leaders who were charged with supporting the learning of middle-grades mathematics teachers across a large US school district. Initial goals for the math leaders' learning included: (a) viewing teachers' improvement of their classroom practices as a progression; (b) designing supports for teachers' learning that were informed by assessments of teachers' current practices, were oriented towards long-term goals for teachers' practices, and would enable teachers to attain short-term goals that constituted reasonable next steps; and (c) facilitating professional development by pressing on teachers' ideas differentially and building on their contributions. Findings suggest that the math leaders increasingly viewed teachers' improvement of their classroom practices as a developmental progression and began to design connected sequences of activities. However, they struggled to facilitate the activities in ways that would meet their ambitious goals for teachers' learning. Based on our findings, we indicate potential improvements to our design for supporting math leaders' learning. More generally, we provide the field with a set of potentially revisable learning goals for math leaders' learning, a set of principles to guide the design of supports for their learning, and a provisional design to support the development of their practices.

This article draws on previously employed methods for conducting fidelity studies and applies them to an evaluation of an unprescribed intervention. We document the process of assessing the fidelity of implementation of the Math Recovery first-grade tutoring program, an unprescribed, diagnostic intervention. We describe how we drew on recent conceptions and standards of fidelity assessment to evaluate the implementation of the program, detailing the process of developing and testing instruments for assessing implementation fidelity, including (a) identifying the intervention's program theory and core components; (b) creating operational definitions of the intervention's core components; (c) developing coding instruments; (d) selecting and training coders; (e) instituting a sampling frame sufficient for generalizing fidelity findings to the study population; and (f) determining the reliability and validity of the data. We also provide a brief overview of the results of the fidelity assessment. We conclude by discussing the aspects of our work that have implications for assessments of fidelity of implementation of unprescribed interventions more generally.

Mathematics Recovery (MR) is designed to identify first graders who are struggling in mathematics and provide them with intensive one-to-one tutoring. We report findings from a 2-year evaluation of MR conducted in 20 elementary schools across five districts in two states. The design allowed for the estimation of the counterfactual growth trajectory based on those students randomly assigned either to a tutoring cohort with a delayed start or to a wait list. Results demonstrate strong end of first grade effects on a diagnostic measure developed by MR and weak to moderate effects (effect size, 0.15-0.30) on measures administered by external evaluators. By the end of second grade, no significant effects were found on any measures. Practical and research implications are discussed. (Contains 7 tables, 3 figures, and 5 notes.)

This chapter describes a partnership with four urban districts that aimed to develop an empirically grounded theory of action for improving the quality of mathematics instruction at scale. Each year, we conducted a data collection, analysis, and feedback cycle in each district that involved documenting the district's improvement strategies, collecting and analyzing data to assess how these strategies were being implemented, reporting the findings to the district, and making recommendations about how the strategies might be revised. We distinguish between two distinct levels of analysis: providing the districts with timely evidence of how their strategies were playing out in schools, and testing and elaborating the conjectures that comprise our theory of action for instructional improvement. We clarify the crucial role that two research tools played at each level of analysis: our emerging theory of action and an interpretive framework that we used to assess the potential of each district's strategies to contribute to instructional improvement. We also illustrate that our collaboration with the four districts instantiates the basic tenets of design-based implementation research and involved conducting systematic inquiry to develop theory related to improving the quality of classroom instruction and student learning at the system level.