Mathematics Coaches Research Articles

Exploring the Discursive Variability of Mathematics Coaches

Research on how coaches talk with teachers during coaching cycles is underdeveloped. We analyzed 1,649 discourse moves from 24 mathematics content-focused coaching cycles to determine the extent to which coaches’ discursive tendencies vary. We explored variation between coaches, between planning and debriefing conversations, and between cycles for the same coach–teacher pair. Findings indicate there existed significant variability in the coaches’ discourse moves during coaching cycles. We also found discursive differences from planning to debriefing meetings, noting that coaches were more directive and less reflective in planning conversations compared with debriefing conversations. Across multiple coaching cycles, we found variation across coaches, with one coach increasing the prevalence of directive moves across four planning conversations and another increasing the prevalence of reflective moves across four debriefing conversations. Although we focus on mathematics coaches, the findings and methodology may be applicable to other disciplines.

Synergistic Collaborations among K-12 Technology, STEM Coaches, and Tech-Industry Partners

This project focused on how two technology coaches, a K-12 Technology Coach and a Science Technology Engineering Mathematics (STEM) Coach collaborated with their coach colleagues and tech-industry partners to offer teachers resources and embedded professional learning (PL). As part of a multiple-case study of coaching models of PL, over the course of two academic years, the researchers gathered observational data during classroom coaching sessions, small group professional learning sessions, and professional development workshops hosted by a tech-industry partner. Additionally, the coaches and a subset of middle school teachers participated in one-on-one interviews and the coaches had discussions in a focus group. Data analyses distilled two main themes: (1) coaches appeal to and collaborate with tech-industry partners; and (2) coaches solicit support and collaborate with school district administrators. Conclusions suggest that technology and STEM coaches serve an integral role in the implementation of technology across the district when collaborating with tech-industry partners. Recommendations include the need for technology coaches to be resourceful and initiate and foster tech-industry partnerships as well as dedicate time to collaborate with other coaches to enhance their own professional knowledge and skills.

An Exploration of How Mathematics Coaches Make Their Own Professional Learning Available to Teachers

Mathematics coaches are often positioned as important mediators between district administrators and teachers regarding messages about ambitious and equitable instruction. Despite this, little research has sought to unpack the connection between what coaches learn at professional development and how they make their learning available to teachers. In this study, we partnered with one district administrator and four mathematics coaches and conducted 15 semi-structured interviews to better understand how these coaches made their professional learning available to teachers. Mathematics coaches emphasized using various structures and resources when making their professional learning available to teachers. Participants also highlighted challenges they encountered when striving to make their learning available. Implications for practice and research are discussed.

Supporting Teacher Learning During Modeled Mathematics Instruction

Although modeling instruction has been identified as a productive professional development activity that coaches can use with teachers in their classrooms, coaches are provided with little guidance regarding how to support teacher learning as they model mathematics instruction. While previous research points to the importance of providing teachers with examples of high-quality instruction through the coach’s model, teachers may need additional support as instruction unfolds to make sense of what they are observing. As part of the current study, I partnered with one mathematics coach and explored how she explicitly sought to augment teacher learning while modeling mathematics instruction. Findings indicate that the coach leveraged three approaches: engaging the teacher in verbal asides during modeled instruction, providing the teacher with written asides in the scripted lesson plan, and scaffolding the observing teacher’s responsibilities. Implications are provided for research and practice.

Identifying and Negotiating Productive Instructional Improvement Goals in One-on-One Mathematics Coaching

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.

Developing Cohesion through Collective Doubting: Framing Practice-Based Professional Learning for Mathematics Coaches

ABSTRACT As instructional leaders who work closely with teachers within and across schools, elementary mathematics specialists (EMS) are positioned well to promote cohesive implementation of impactful pedagogy throughout school districts. However, EMS’s work can be impeded if they do not have structured opportunities to collectively grapple with the nuances of terminology included in teaching and learning initiatives in terms of expectations for what practices look like within classrooms. Using narrative data collected from EMS team discussions about the meaning of student engagement in mathematics classrooms, we share a five-phase framework for using a collective doubting process to promote professional learning through the development of shared understanding of common language. By positioning moments of doubt as opportunities for collaborative learning, this framework serves as a flexible structure to guide the development of knowledge-in-practice from the identification of a practice-centered inquiry goal to cohesive understanding and systemic transformation.

Examining a Coaching Routine to Support Teacher Learning

ABSTRACT Mathematics specialists tasked with the responsibility of supporting teacher learning face both the opportunity and the challenge of transforming the organization of the school workplace to support educators’ collective, ongoing learning, which is not the norm in most school settings. In this study, we examine a coaching routine called Teacher Time Out (TTO), which was organically developed by a school-based mathematics coach and the teachers with whom she worked. Through the routine, coaches and teachers work through complex, in-the-moment pedagogical decision making while collectively facilitating mathematics discussions among students. The routine thus opens opportunities for educators to learn about ambitious teaching alongside their colleagues. We report findings from an analysis of 360 TTOs that occurred over three years of one coach’s work supporting a school-wide, multi-year instructional reform effort in mathematics teaching and learning. We found that the coaching routine fostered teachers’ collective inquiry into practice, as they engaged with the unpredictability of teaching during real-time instruction with students. We discuss the potential of this routine to support coaching as a lever for organizational reform, reshaping mathematics teaching across many classrooms.

Collaborative and Sustained Professional Development With Mathematics Coaches

To encourage growth in instructional practice, the authors describe various formats, plans, and scheduling options for mathematics coaches and other stakeholders to consider when determining effective ways to enhance the teaching and learning of mathematics.

Researchers as Coaches: Developing Mathematics Teaching Capacity Using MEAs for STEM Integration

ABSTRACT The purpose of this study was to explore how university researcher professional development design decisions built and sustained K-8 partnerships which foregrounded mathematics in integrated STEM via model-eliciting activities (MEAs). We applied a self-study methodology to facilitate a longitudinal examination of our practice in this multi-year project. We used the Decision-Making Protocol for Mathematics Coaching to understand our collaboration with division stakeholders as they worked toward integrating MEAs with district curriculum and pacing. Analysis of professional development artifacts, evidence of scholarship, and researcher memos revealed four recalibration points driven by district initiatives and leadership changes. Coaching with MEAs created opportunities for equitable student engagement and formative assessment. Implications for designing professional development that emphasizes explicit connections between the constraints of mathematics curriculum and the possibilities of teaching and learning through STEM integration are presented.

Learning to design effective professional development: The influence of integrating a coaching tool with an elementary mathematics specialist course assignment

As content-specific educational coaches, elementary mathematics specialists (EMSs) have emerged as school-based professionals who are needs-driven and work closely with school stakeholders in regard to mathematics teaching and learning. While leading mathematics education organizations have identified the specialized knowledge and skills required for EMS positions, how to best prepare these individuals is knowledge that the field is still exploring. This paper first presents a theoretical model for EMS preparation that aligns an emerging coaching tool, the Decision-Making Protocol for Mathematics Coaching (Baker & Knapp, 2019, [DMPMC]) with the Professional Development Design Framework (Loucks-Horsley et al. in Designing professional development for teachers of science and mathematics, Corwin Press, 2010). The paper then presents a descriptive case study that examines the application of this model in an EMS preparation course. The findings indicate that assessing the coaching situation fostered administrative partnerships, revisiting goals increased specificity of anticipated outcomes, and applying research-informed practices increased EMS self-efficacy and advanced coaching agendas. Taken together, these findings suggest that integrating the DMPMC into an EMS preparation course led to positive changes in EMS candidate learning of professional development design. Notably, this is one of the first studies that documents the influence of a coaching education tool on EMS candidates’ professional development design.

Mathematics Teachers’ Perceptions of Practice: A Q-Methodology Study

The instructional practices enacted by mathematics teachers have the most powerful impact on students’ learning. In our study, we analyzed mathematics teachers’ perceptions of their instructional practices, specifically related to their use of actions that support high-leverage practices. Q Methodology was used to investigate the divergent perceptions of mathematics teachers’ teaching practices. Employing principal component analysis with varimax rotation, five factors were extracted that represented the perceptions held by 38 elementary, middle-level, and high school teachers from Pennsylvania, North Carolina, and Mississippi. We identified the five factors as: Promoting Students’ Productivity; Using High-Level Tasks; Promoting Sense-Making and Reasoning; Encouraging Mathematical Representation; and Acknowledging Students in Time. The mathematics teachers’ perceptions of their teaching actions that support high-leverage practices will benefit mathematics coaches, mathematics educators, professional development providers, and the teachers themselves.

Exploring Relationships Among Responsibilities of Mathematics Coaches and Specialists and Student Achievement

In this study, we used hierarchical linear modeling to examine restricted-use 2011 National Assessment of Educational Progress (NAEP) data to explore relationships between principal-reported time spent on the different NAEP responsibilities of mathematics coaches and specialists (MCSs) and the achievement scores of approximately 37,400 fourth-grade students in 1,500 U.S. elementary schools. The model included adjustments for composite covariates, control variables, and sampling weights. Significant relationships between principal-reported time spent on six different NAEP-defined responsibilities provided by full-time MCSs and fourth-grade students’ mathematics achievement were observed, including relationships between achievement and MCSs assisting both teachers and students. Implications for the effective use of MCSs in schools and suggestions for future research are discussed.

Considering Possibilities to Promote Disciplinary Literacy Instruction in Mathematics

AbstractIn this article, we use a case study to provide suggestions and lessons for considering mathematical literacy instruction. Preservice teachers in the study were provided coursework and support in designing mathematical literacy instruction, and then they incorporated that instruction into a field‐based practicum experience. We then studied their perceptions to consider how teachers might be supported in mathematical literacy instruction. Themes that emerged from analysis focused on the role of mathematical literacy in mathematics instruction, complexities of instantiating inquiry in mathematics instruction, and linking teacher education in mathematical literacy to the realities of secondary mathematics curricula and schooling. Findings are presented in the form of lessons gleaned from these themes that teachers, mathematics coaches, and teacher educators might use to provide support for mathematical literacy instruction and integration.

Book Review: Mathematics Coaching & Collaboration in a PLC at Work. Every Student Can Learn Mathematics

Book Review

Coaching in Context: Exploring Conditions that Shape Instructional Coaching Practice

Background/Context The literature shows that one constant in coaching is the high degree of variation in coach roles and contexts, suggesting that understanding coaching practice requires that we also understand the role structures and organizational conditions that shape coaches’ work. Research on both instructional coaching and instructional change is increasingly attending to the organizational and social factors that shape, facilitate, and constrain the web of interactions that coaching work comprises. Past research points to the complex systems and social networks that shape critical elements of coaching practice, emphasizing the interdependency of organizational processes and the critical importance of considering not only the outcomes of implementation, but also the contextual factors that shape them. Purpose/Objective/Research Question/Focus of Study Given that multilayered social, technical, and organizational factors shape the practice and impact of instructional coaching, understanding the combinations of factors that are most consequential is key for both policy implementation and instructional coaching research. Consequently, understanding coaching requires attending to specific practices, the structural contexts in which those practices are embedded, and varied implementation processes across system levels and diverse school districts. Therefore, we built this study on the foundational idea that coaching work inherently and continuously interacts with the complex systems in which it takes place and that understanding and analyzing coaching requires attending to the organizational and social structures that shape it. Accordingly, this article focuses on the following research question: What contextual conditions facilitate and constrain coaching, and why? Research Design To understand the interactions between coaching work and these many social and technical factors, we investigated how a group of coaches implemented a mathematics coaching model, focusing specifically on the relationship between coaching contexts and coaching practice. Our case-focused, mixed-methods approach, which included both qualitative comparative analysis (QCA) and case-study methods, allowed us to explore the interrelationships between coaching and the system conditions that shape, enable, and constrain instructional change. Conclusions/Recommendations Our findings support the argument that coaching cannot be extricated from the surrounding system factors that shape it. On the contrary, we found that supports for and barriers to robust coaching practice are context-specific phenomena, suggesting that any coaching intervention ought to be tailored to its specific organizational location. Accordingly, we argue that different combinations of contributing factors can affect coaching in different ways, thereby contributing to the theory that a nested-systems perspective on instructional coaching is key to understanding its effects.

Mathematics Coaching for Conceptual Understanding: Promising Evidence Regarding the Tennessee Math Coaching Model

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.

Mathematics Specialists as the Hidden Players in Professional Development: Researchable Questions and Methodological Considerations

This paper suggests implications for researchable questions about mathematics teacher development. We ask the following: what is necessary for research that includes mathematics specialists or other hidden school-based roles within a project beyond classroom teachers and students? Mathematics specialists (e.g. mathematics coaches, mathematics teacher leaders) support teacher learning and development using different models of school-based professional development. They can play a critical role in connecting research and practice. However, research in mathematics education has regularly neglected to examine their role in studies of professional development. We suggest there are two needs for creating and examining researchable questions about such hidden players in studies of professional development: (1) defining practices and hidden players involved in systematic school change and (2) identifying the unit of analysis and scaling up professional development. We summarize existing studies and present considerations for future research.

The development of instructional guidelines for elementary mathematical writing

AbstractMathematical writing recently has been defined as writing to reason and communicate mathematically. But mathematics instructional resources lack guidance for teachers as to how to implement such writing. The purpose of this paper is to describe how methods of design‐based research were used to develop an instructional resource when one does not currently exist. Thirty‐four participants—including teachers, mathematics coaches, mathematics curriculum developers, literacy coaches, a mathematician, and academics in elementary mathematics education, mathematics education, writing education, and science education—participated in a multi‐step process to recommend, revise, and confirm instructional guidelines for elementary mathematical writing. The development process began with thirty‐two recommendations from science writing and language arts writing. Through multiple cycles of feedback, five instructional guidelines and related considerations and techniques for implementation of elementary mathematical writing emerged.

Math and English language development: MELDing content and academic language for English learners

ABSTRACTProject Mathematics and English Language Development (MELD) is a sixth-grade mathematics intervention aimed at supporting English learners’ (ELs) development of academic language and mathematical knowledge. This article describes the MELD scaffolds and strategies for ELs with multiple examples, as well as survey and focus group data on the effectiveness of the scaffolds and strategies. The article is written for mathematics teachers and coaches who work with ELs so that they can apply the scaffolds and strategies to their curricula.

Learning From Adaptation to Support Instructional Improvement at Scale: Understanding Coach Adaptation in the TN Mathematics Coaching Project

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.