Equity-Focused, Rubric-Based Coaching: An Incremental Improvement Approach to Supporting Teachers to Shift Toward More Equitable Mathematics Instruction

Abstract

Historically, inequities in mathematics education have resulted in mathematics classrooms that do not support all students, and particularly students from marginalized backgrounds. Efforts to transform mathematics classrooms to be culturally responsive, sustaining, and justice-oriented have met limited success at scale. It may be that supporting teachers to develop more equitable teaching practices would benefit from a more incremental improvement approach. This article considers how school-based mathematics coaches can support teachers to make incremental shifts toward more equitable instruction. We describe a coaching model designed to include elements of incremental improvement, in which coaches and teachers analyze video against a set of rubrics that delineate equitable teaching practices. Using established routines and structures, coaches and teachers work together to identify and enact small, actionable changes that build toward more ambitious equity-oriented practices. Drawing on pilot data, we articulate how the coaching model both reflects and builds on an improvement approach to professional learning. We argue that while incremental shifts may be insufficient to fully address systemic inequities, they can serve as a meaningful bridge toward larger changes. We conclude with considerations for engaging in equity-oriented incremental improvement work.

1. Introduction

Mathematics classrooms can function as both supportive and marginalizing spaces for students. Supportive mathematics classrooms are equitable, responsive, and culturally and mathematically affirming and are characterized by strong relationships, high expectations and responsive teaching (Abdulrahim & Orosco, 2020; Comstock et al., 2023). Mathematically, they provide students with access to rigorous mathematics, support students’ mathematical thinking, and leverage and affirm students’ cultural and mathematical identities (Comstock et al., 2023; Gutiérrez, 2012; Ladson-Billings, 1997). Yet evidence suggests that classrooms such as these are not the norm, especially for Black and Latine students (Boston & Wilhelm, 2017). Students from minoritized racial and ethnic backgrounds experience weaker teacher–student relationships (Bottiani et al., 2016) as well as lowered expectations, reduced cognitive challenge, and teachers’ racial bias in instructional decision-making (Boston & Wilhelm, 2017; Coppersmith et al., 2024; Harber et al., 2012; TNTP, 2018). Even when mathematics instruction incorporates ambitious teaching practices, it is not always equitable (Jackson & Cobb, 2010).

Calls for more equitable mathematics education have emphasized how teachers might enact culturally relevant or sustaining teaching practices or integrate math with social justice (Comstock et al., 2023; Kokka, 2019). Classrooms in which historically marginalized students excel affirm students’ cultural and mathematical identities, make expectations for mathematical activity both high and explicit, and provide mathematical and social support (Wilson et al., 2019). However, evidence suggests that this type of teaching represents a significant departure from current practice and mathematics teachers may need support to deepen their instruction along these lines (Hill et al., 2018; Wilson et al., 2019). While impediments to adoption may include accountability pressures or other contextual factors, such teaching may also require large shifts in teachers’ dispositions and beliefs, as well as their skills and knowledge.

One way to support teachers to enact more equitable mathematics teaching practices may be to take a more incremental approach to improving instruction (Litke, 2020a; Otten et al., 2022; Star, 2016). Incremental approaches target smaller shifts in practice that build and bridge to more ambitious changes. Incremental improvement approaches begin with teachers’ current practice, incorporate modest and actionable improvement goals, consider teachers’ classroom context, focus on specific teaching practices that may not be widely enacted, and advocate for gradual changes. In theory, it is the accumulation of these smaller changes that work to shift practice. In the context of equitable mathematics teaching, such incremental changes may be insufficient for disrupting long-standing inequities in mathematics education (e.g., Martin, 2019). However, while the field must continue to push for culturally responsive and sustaining mathematics teaching, given evidence that such pedagogies are not widely enacted (Comstock et al., 2023), we argue that in addition, we can support teachers to make smaller shifts that move practice toward more equitable teaching.

Instructional coaching may be particularly suited to incremental improvement; coaches work directly and regularly with teachers, have content and contextual knowledge, and can provide targeted support around finer-grained practices in ways that are grounded in teachers’ current practice and context. Individualized and sustained coaching around improving aspects of mathematics instruction can positively impact both instructional quality and student achievement (Campbell & Malkus, 2011; Kraft et al., 2018; Kraft & Hill, 2020). Reviews of equity-focused professional learning suggest that these efforts may lack instructional or subject-matter specificity (Bottiani et al., 2016; Parkhouse et al., 2019); coaching around mathematics-focused equitable teaching practices may address these issues and thus allow teachers to more easily translate what they learn into practice.

Our goal in this article is to illustrate how one model of mathematics coaching focused on more equitable mathematics teaching reflects an incremental approach. In doing so, we consider the ways in which lessons from the incremental change literature can inform program design and highlight how the model’s enactment expands on and provides specificity to elements of incremental change. We describe Honoring Equity and Access: Rubrics for Mathematics Instruction (HEAR-MI) Coaching, a coaching model leverages video analysis using the Equity and Access Rubrics for Mathematics Instruction (EAR-MI), a set of empirically grounded classroom observation rubrics (Wilson, 2022) alongside coaching routines and structures. In HEAR-MI Coaching, coaches and teachers work collaboratively through cycles of goal setting, video analysis, and reflection. The model (a) engages teachers in setting their own improvement goals, (b) introduces teachers to research-aligned practices that serve as a shared language and external standard, (c) includes routines and structures designed to support teacher learning of specific aspects of equitable teaching practices, and (d) allows teachers to build on current practice to integrate this new learning through smaller adjustments.

In what follows, we first describe our conceptualization of incremental improvement approaches, identify the teaching practices underlying HEAR-MI Coaching, and outline how coaching can support incremental improvement efforts. Next, we describe the model itself. We draw on the reflections of teachers who participated in a pilot study of HEAR-MI Coaching to delineate the ways in which the model’s components reflect incremental improvement and to further our understanding of such approaches. By articulating how HEAR-MI Coaching both builds from and contributes to the incremental improvement literature, we seek to articulate design elements that support others engaged in this work. We conclude with a discussion of how incremental improvement approaches can support teacher learning around equitable teaching practices and raise considerations for the field around engaging in equity-oriented incremental improvement.

2. Perspectives

2.1. Features of Incremental Approaches to Improving Mathematics Teaching

Despite long-standing calls for mathematics instruction to shift toward student-centered, ambitious, and conceptually oriented approaches, large-scale investigations into teaching practices have shown that teacher-directed, didactic, and procedurally focused instruction persists (Hiebert et al., 2005; Kane & Staiger, 2012; Litke, 2020b; Wilson et al., 2019). This is particularly true in classrooms serving large percentages of minoritized students (Boston & Wilhelm, 2017). Professional development efforts have shown limited success at supporting teachers to make meaningful and lasting shifts toward ambitious teaching, with teachers often grafting reform ideas onto existing practice, limiting positive impacts for students (Cohen, 1990; Otten et al., 2022).

As a result, scholars have begun to consider whether professional learning might more effectively support teachers to make incremental, rather than wholesale, changes to instruction (Janssen et al., 2015; Litke, 2020a; Otten et al., 2022; Star, 2016). Key considerations for designing such professional learning include determining both the focus of the professional learning (e.g., what instructional practices could be best leveraged through an incremental approach) and the activities that support teachers to build on their practice in incremental ways. To achieve this, it is necessary to understand the principles behind incremental improvement approaches.

One key feature of incremental improvement approaches is that they center smaller, finer-grained practices that support student learning, but may not be widely enacted or may not be enacted deeply (Star, 2016). These practices can be embedded in existing instructional modalities (Litke, 2020a; Star, 2016), facilitating uptake. For example, Litke (2020a) identified specific teaching practices that support students’ learning opportunities in algebra (e.g., supporting procedural flexibility or connecting across mathematical representations), demonstrating how they might be leveraged to promote more student voice and discussion in teacher-centered classrooms. A focus on finer grained features of instruction can “open a door within teachers’ practice for more ambitious instructional changes in the future” (Star, 2016, p. 59). Practices that are likely to be taken up by teachers are congruent with existing practice, include clear articulations of teacher actions, and are those in which teachers see value and benefit (de Araujo et al., 2022; Janssen et al., 2015). We suggest that a focus on fine-grained, high-uptake practices that support more equitable mathematics classrooms may serve as a bridge toward more “ambitious” equitable teaching practices, allowing teachers to build their skills and knowledge for engaging in this work.

A second feature of incremental improvement approaches is a focus on small adjustments rather than wholesale changes to instruction (Otten et al., 2022; Star, 2016). For example, some advocate for small suggestions or nudges (Otten et al., 2022), providing bite-size changes that are easy to take up and integrate into existing practice. A focus on smaller changes can support teachers to see improvement efforts as practical and actionable (de Araujo et al., 2022; Janssen et al., 2013), increasing the likelihood they are adopted. The accumulation of multiple smaller shifts can also serve as a bridge from current to sought-after practices (Janssen et al., 2013; Litke, 2020a; Otten et al., 2022).

Finally, such approaches are grounded in teachers’ current practice. Incremental approaches that reflect more modest (and realistic) goals are attuned to teachers’ contexts and constraints (Otten et al., 2022). For example, in higher education settings, rather than asking instructors to abandon traditional lecture for active learning, professional development focused on “active lecture” reflect less of a departure from current practices and may support instructors to develop skills and dispositions needed to shift toward more student-centered approaches (He, 2021). Furthermore, adapting or building on existing practice through incremental steps meets teachers where they are, supporting buy-in and enactment (Davis et al., 2016; Janssen et al., 2015; Litke, 2020a; Otten et al., 2022). Given evidence that mathematics classrooms—and particularly those with high percentages of students from historically marginalized backgrounds—may not widely feature equitable teaching practices (e.g., Comstock et al., 2023; Wilhelm et al., 2023), understanding and building on teachers’ extant practice with smaller adjustments focused on fine-grained teaching practices may be a promising approach.

2.2. Descriptions of Equity-Focused Instructional Practice in Mathematics

Mathematics education research has focused on supporting teachers to enact ambitious teaching practices (Lampert et al., 2010, 2013). However, while ambitious teaching can support equitable outcomes and opportunities (Kang, 2022), it can also be enacted in ways that reinforce or worsen inequities (Nasir et al., 2008). Researchers focused specifically on equitable teaching have identified teaching principles that support students who have been historically marginalized in school. These include building students’ academic and social-emotional skills, affirming students’ social and cultural histories, and preparing students to recognize, analyze, and address inequality. In such classrooms, teachers hold high expectations for students, express commitment to students’ learning, and demonstrate respect for students’ knowledge and agency (Ladson-Billings, 1995; Milner, 2011; Siddle Walker, 1993; Tate, 1995; Ware, 2006). In mathematics, such teaching incorporates a greater focus on students’ cultural backgrounds, identities, and funds of knowledge, supports students to use mathematics to address and respond to social injustice, and encourages students to question whose mathematics matters (Abdulrahim & Orosco, 2020). However, evidence suggests that such critical or culturally sustaining pedagogies are not the norm in mathematics classrooms, are challenging for teachers to enact, and come with barriers to implementation (Comstock et al., 2023; Cruz et al., 2020).

It may be fruitful to identify finer-grained teaching practices that can, through smaller adjustments, build on teachers’ existing practice and potentially bridge to the more critical practices described above. To achieve this, we draw on a set of mathematics-focused teaching practices that research has shown to support equitable outcomes for historically marginalized students (Wilson et al., 2019). Drawing on data from the Middle School Mathematics and the Institutional Setting of Teaching study, researchers identified classrooms that successfully supported African American students’ mathematics achievement. Analyzing video recordings of mathematics lessons and scores from the Instructional Quality Assessment, the authors held constant conceptually oriented teaching and identified equity-focused instructional practices that characterized these classrooms. Notably, these practices were not as present in conceptually oriented classrooms in which African American students did not thrive. While the full set of practices are described in depth in Wilson et al. (2019), for the purposes of this article, we focus on a sub-set of these practices (see Figure 1) that formed the basis of our coaching model.

In these more equitable mathematics classrooms, teachers attended to classroom community, explicitly focusing on building and maintaining productive learning environments (Wilson et al., 2019). Teachers achieved this by proactively building relationships and productive classroom culture through connecting with students and reinforcing classroom values. Teachers also attended to classroom environment in how they reactively responded to apparent off-task behavior, leading with curiosity and determining students’ needs while also re-engaging students in mathematics. In addition, teachers positioned students as competent, making public statements that indicated that they valued students’ mathematical thinking and contributions to the learning community. Rather than making blanket statements about the class’s ability level or competence, teachers carefully and intentionally identified individual students’ contributions, noting what about that contribution was mathematically important and making visible to the class how the contribution supported mathematical learning. Teachers also set clear, explicit expectations for students’ social and mathematical behavior. In doing so, teachers carefully articulated what they expected of students mathematically in relationship to a mathematical task and what they expected socially in terms of how they expected students to work together on these tasks. Teachers thus made visible the often-unwritten rules of the mathematics classroom. Finally, these teachers attributed mathematical responsibility to students in response to requests for assistance, transitioning authority for mathematical problem-solving and decision-making away from themselves and onto students. Specifically, teachers pushed back on students’ requests for help, directing them to consult with peers or leverage other resources at their disposal (e.g., their notes, anchor charts, etc.). In doing so, they explicitly encouraged students to persist in solving problems and normalized productive mathematical struggle as part of the learning process, fostering student thinking and independence.

The practices described above reflect only a subset of those that the field has suggested comprise equitable mathematics teaching. We do not argue that these are the only—or even the most effective—equitable teaching practices in mathematics, but rather highlight them because they are a relatively small grain-size, have been shown to support student learning and success, and lend themselves to the smaller adjustments to practice advocated for in incremental approaches. In addition, these practices have been developed into a classroom observation tool, the EAR-MI (Wilson, 2022), which provides guidance for what “good, better, and best” enactments might entail. Observation rubrics have been used in coaching models to support teachers to shift practice (Kraft & Hill, 2020) and the EAR-MI is a central component of HEAR-MI Coaching.

2.3. Coaching as a Lever for Incremental Improvement

Instructional coaching is a form of job-embedded professional learning that consists of regular contact between teachers and coaches knowledgeable in content and pedagogy for the purpose of improving instruction (Mangin & Dunsmore, 2015). We see mathematics coaching as a particularly promising mechanism for incremental improvement approaches to professional learning. Most U.S. schools have access to an instructional coach (National Center for Education Statistics, 2020), making it possible to integrate coaching into the regular work of teachers in schools. Furthermore, mathematics coaching has the potential to support teachers to enact equitable teaching practices through coaches’ situated knowledge of school contexts and students’ backgrounds and strengths (Marshall & Buenrostro, 2021).

Coaching activities vary in form and structure (Campbell & Malkus, 2011). In mathematics, individualized, intensive, and sustained coaching work with teachers has shown positive benefits on both instructional practice (Kraft et al., 2018) and student achievement (Campbell & Malkus, 2011). Specifically, coaching that centers in-depth, focused conversations about mathematics content, pedagogical practice, and student learning can support teachers’ growth and development (Russell et al., 2020). Effective coaching conversations feature specificity, depth, and a connection between teacher, student, and mathematical content (Russell et al., 2020). Gibbons and Cobb (2016) highlight the importance of goal setting, analysis of current practice within a trajectory of pedagogical development, and the co-construction of action steps for improvement.

One increasingly common activity in mathematics coaching is to ground coaching conversations in the analysis of video recordings of classroom instruction. Video serves as an artifact of classroom instruction, can be paused, rewatched, and decomposed, and clips can be selected to focus on a particular practice or purpose (Borko et al., 2008). Video analysis can foster productive discussions focused on teaching and learning. Video has been used in professional learning as a tool to support teachers’ professional noticing (Amador et al., 2023), facilitating teachers to identify and reflect on critical instructional moments (van Es & Sherin, 2021) and attend to student thinking (Walkoe, 2015). Studies of coaching models that incorporate video analysis find that such activities can support teachers to notice both positive enactments of and opportunities for growth around specific instructional practices (Suh et al., 2021). When teachers analyze video from their own classroom, they can situate pedagogical reflection in their own context, supporting a close connection to practice. However, some teachers may be hesitant to engage in this self-reflection; video analysis of instruction from unknown teachers can promote participation and engagement in instructional improvement conversations (Beisiegel et al., 2018). Video from unknown teachers may de-personalize coaching conversations, allowing coaches or facilitators to foreground specific aspects of practice for discussion.

Some coaching models use classroom observation rubrics as a lens through which to engage in video analysis (e.g., Beisiegel et al., 2018; Kraft & Hill, 2020). Grounding video analysis in an observation rubric can support teachers to both learn aspects of the effective teaching practices highlighted by the tool and strengthen enactment of these practices (Kraft & Hill, 2020).

2.4. The Current Paper

In this article, we describe HEAR-MI Coaching, a model that was developed as part of a National Science Foundation-funded project with the goal of supporting middle school teachers to enact more equitable mathematics instruction. HEAR-MI Coaching integrates conversational routines and activities from an effective, video-based coaching model (Kraft & Hill, 2020) with a set of empirically developed, validated classroom observation rubrics focused on equitable mathematics teaching practices (EAR-MI; Wilson, 2022). The theory of action for HEAR-MI Coaching posits that if teachers work directly with coaches to learn to analyze instruction using EAR-MI, they will deepen their instruction in ways that align with EAR-MI practices and better support students’ learning and success, particularly for those students who have been historically underserved in mathematics classrooms. We designed HEAR-MI Coaching to take an incremental approach, using video analysis to ground coaching conversations in teachers’ existing practice and leveraging the EAR-MI to support teachers to make small, manageable shifts to their teaching. Drawing from teachers’ experiences in the pilot year of HEAR-MI Coaching, we seek to illustrate features of the model that both reflect and build on elements of incremental improvement approaches. Specifically, we ask the following question: How does an equity-focused coaching model instantiate and elaborate guidance about incremental improvement?

3. Materials and Methods

We piloted HEAR-MI Coaching with four mathematics coaches from four different schools in a very large, urban school district in the western part of the U.S. The district serves students who are majority Hispanic or Latine, and the participating schools largely mirrored the district demographics. Participating coaches worked full-time in middle schools, supporting teachers around mathematics instruction specifically. To recruit the participating coaches, the research team collaborated with an external organization that provided support to district schools. The coaches had 4–8 years of coaching experience, and all had taught mathematics prior to becoming coaches. Each coach selected 2–3 teachers in their school to pilot HEAR-MI Coaching (10 teachers total). Participating teachers taught middle school math (6th, 7th, or 8th grade) and ranged from novice (first year teacher) to experienced (8 years).

In the summer prior to the pilot year, coaches participated in a four-day training session in which project staff supported coaches to learn the EAR-MI, the model, and the coaching routines. In this training, coaches used EAR-MI to engage in video analysis of video clips from our project library. They learned the HEAR-MI Coaching cycle (described below) and engaged in role plays of coaching conversations. Through these activities, they participated in discussions around issues that might arise during HEAR-MI Coaching. During the school year, coaches and teachers worked together to enact multiple coaching cycles. Coaches received ongoing support from project staff through monthly webinars and one-on-one check-ins as needed. Webinars included analysis of coaching conversations, clarification around EAR-MI rubrics, and discussions of common issues that arose during coaching.

One goal of the pilot was to understand how coaches and teachers perceived and experienced HEAR-MI Coaching. We conducted two 45–60 min semi-structured interviews with all participating teachers at the beginning and end of the school year. End of year interviews asked teachers to reflect on their experiences with HEAR-MI Coaching, with the specific EAR-MI rubric they had selected as a focus for coaching, and how HEAR-MI Coaching influenced their thinking about their teaching. Data analysis is ongoing; however, we draw on teacher interviews to illustrate the ways in which the model takes an incremental approach to improving teaching and to identify additional elements that support such an approach. To achieve this, we mapped the elements of HEAR-MI Coaching to the features of incremental improvement. We then analyzed interview transcripts, identifying when teachers themselves noted incremental improvement elements in the coaching model and identifying additional aspects that could inform incremental improvement. In what follows, we first describe the HEAR-MI Coaching model as it was designed. Next, we draw on the interview data to illustrate how HEAR-MI Coaching both reflects an incremental approach to supporting teacher learning and adds to our understanding of what incremental improvement approaches may entail.

4. Findings

4.1. The HEAR-MI Coaching Model: Designed for Incrementnal Improvement

In HEAR-MI Coaching, teachers work with instructional coaches knowledgeable about equity and instruction. Prior to beginning coaching cycles, the teacher and coach have an introductory meeting in which the coach shares an overview of each of the EAR-MI rubrics and the teacher articulates a problem of practice or improvement goal of interest to them. Working together, the teacher selects one EAR-MI rubric that they perceive to be aligned with their improvement goals as the focus of the first coaching cycle. For example, a teacher may share with their coach that one of their goals is for their students to become more independent and less reliant on the teacher for guidance. Through discussion, the coach and teacher may collaboratively decide to work with Attributing Responsibility to Students in Response to Student Requests for Assistance, an EAR-MI rubric that focuses on supporting teachers to shift mathematical authority and agency onto students, while holding students accountable for their learning. Coaches and teachers then follow a five-step cyclical process of analysis and reflection (see Figure 2). We describe this process in detail below.

First, the teacher video records a lesson from their own classroom and shares the recording with their coach (Step 1). The coach reviews the lesson video recorded by the teacher and selects one to two short video clips from that lesson to use in the coaching conversation (Step 2). In addition, the coach selects one to two video clips from the project’s video library that support analysis and reflection around the focal EAR-MI rubric. The use of clips from our video library allows coaches and teachers to deepen their understanding of teaching practices, while video clips from the teachers’ own classroom allow for a direct connection between video analysis and teacher’s context and practice.

Next, the teacher watches the selected clips, considering each in light of the focal EAR-MI rubric (Step 3). The coach and teacher engage in a coaching conversation using a coaching routine we call describe and elevate (Step 4). The purpose of this two-part routine is to support the teacher to better understand and operationalize EAR-MI practices and calibrate their analysis of teaching to the rubric standards. The routine provides structure to discussions of teaching, encourages self-reflection, and seeds actionable steps for the teacher’s own practice related to their improvement goal. The coach and teacher enact the routine first using video clips from the project’s video library. This both depersonalizes the instructional analysis and allows the teacher an opportunity to better familiarize themselves with the components of the EAR-MI practice before turning attention to video from their own classroom. After analyzing one to two clips from our project’s video library, the coach and teacher repeat the process with video clips from the teacher’s classroom.

During the describe portion of the routine, the teacher and coach watch and discuss the video clip through the lens of the focal EAR-MI rubric. They do this by identifying instructional moments in the clip that feature instantiations of the focal practice, using the rubric’s indicators and evidence from the video transcript to guide the discussion and support their analysis. Specifically, the coach and teacher draw on the rubric’s definition and anchoring questions to identify and mark transcript excerpts that illustrate opportunities for the focal EAR-MI practice. Then, they use the rubric indicators to consider where the clip might fall along a continuum for the given practice, focusing on finer grained aspects of the practice associated with varying levels of enactment.

For example, in a coaching conversation focused on the Positioning Students as Competent, the coach and teacher might first consider how the rubric defines the practice (e.g., providing a specific affirmation for what student did mathematically and providing a rationale for why the contribution was valuable). The coached teacher might next identify instances in which the teacher in the video marks a student’s contribution as contributing to the learning community. The coach might then highlight that portion of the lesson transcript. Drawing on the rubric, the coach may ask the teacher to consider the extent to which the video clip showed evidence that the highlighted affirmation was specific and included a clear rationale for why the student’s contribution was productive. The coach and teacher might then describe the depth which this practice was enacted in the video, using indicators from the rubric. For example, they might consider whether the teacher simply praised a student contribution with a statement such as, “Good job” (lower-level enactment) or whether the enactment moved beyond marking to provide specificity about what was productive about the student contribution and/or a rationale for why the contribution was productive and connects to disciplinary practices in mathematics (higher level enactment).

The conversation then shifts to the elevate portion of the routine, in which the coach and teacher discuss ways to deepen the highlighted transcript interactions, grounded in the rubric indicators. This discussion focuses on how the instruction in the clip might, through small adjustments related to rubric indicators, shift toward more in-depth enactments of the practice. This portion of the conversation is framed around the idea that there is no such thing as “perfect” instruction, acknowledging that teaching is a continual process of reflection and improvement. Thus, the focus is not on improving the teacher’s “score” on the rubric, but rather on specific, actionable elevations that improve learning opportunities for students. Importantly, the coach and teacher do not revamp the lesson entirely, rather they begin from the instruction as is, revising and adding on to teacher and student interactions.

As part of this discussion, the coach and teacher collaboratively mark the transcript, inserting additions, alternative phrasing, or other possibilities as they discuss them. For example, in the elevate portion of a discussion focusing on the Positioning rubric, the coach and teacher might look at a transcript segment in which the teacher marked a student’s contribution with a broad affirmation such as, “Good job with the triangles” and consider what the teacher might add to this affirmation to provide specificity and a rationale (e.g., “Good job—I like how you broke the rectangle in half to show that it was made of two triangles as a way to prove that the area of the triangle was half the area of the rectangle. That kind of modeling is important because it allows us to make sense of formulas”).

Finally, after analyzing the video clips and engaging in two to three describe and elevate discussions, the teacher reflects on the conversation, identifying specific goals for their next cycle and developing action steps for their own teaching (Step 5). These action steps are determined through discussion between the teacher and the coach, and the teacher commits to a plan for their enactment. Examples of goals and action steps include intentional planning for ways to surface the focal EAR-MI practice, goals related to a particular part of the lesson (e.g., enacting a practice during the launch of a mathematical task or the whole group discussion following work on a task), or goals related to specific aspects of the focal rubric (e.g., providing specificity or a rationale). The action steps also serve to seed a new coaching cycle, with the teacher planning to record a new video for the next discussion.

Several aspects of HEAR-MI Coaching were designed to align with an incremental improvement approach to professional learning. First, the model focuses on specific, research-backed teaching practices that do not feature widely in classrooms. The EAR-MI rubrics support coaches and teachers to decompose the practices into their component parts. As such, they provide specificity for instructional shifts, provide coaches and teachers with common language, and calibrate discussions of teaching to an external standard. Selecting a single EAR-MI rubric for a coaching cycle allows teachers and coaches to focus their instructional improvement work around deepening one practice at a time. Second, the model was designed to emphasize small adjustments to practice. Through the describe and elevate routine, coaches and teachers annotate the transcript with additions and suggestions but do not redesign the lesson. Similarly, teachers’ goal setting and action steps are focused on smaller adjustments rather than wholesale reform. The coaching conversations are grounded in moving from “good” to “better” rather than targeting a “best” level of practice. Finally, HEAR-MI Coaching is designed to build from and deepen teachers’ current practice. Teachers begin by identifying an improvement goal stemming from their practice. By integrating video clips from teachers’ own classrooms into the describe and elevate routine, instructional improvement conversations are grounded in teachers’ existing contexts. Similarly, teachers articulate action steps for their own planning and instruction based on the coaching conversations.

4.2. Teachers’ Experiences with HEAR-MI Coaching: Developing Our Understanding of Incremental Improvement Approaches

We were interested in what aspects of HEAR-MI Coaching participating teachers identified as facilitating incremental changes to teaching practice. In interviews, we asked teachers to describe how HEAR-MI Coaching supported them to reflect on and improve their teaching. When teachers’ responses identified specific features of incremental improvement (e.g., fine-grained practices, small adjustments, building from current practice), we sought to understand what aspects of the coaching model they found salient. Our goal in doing so was to build our understanding of design elements that can support incremental improvement. Teachers highlighted how grounding coaching conversations in the EAR-MI facilitated them to build on their current practice. By decomposing the focal practices into component parts, the rubrics provided specificity that made it possible for them to enact concrete instructional changes. Teachers also noted how the use of structured coaching conversations—specifically the analysis of video clips using the describe and elevate routine—supported them to make small adjustments to their own teaching. Finally, teachers emphasized how choice both in setting goals and in rubric selection, allowed the coaching to connect to and build upon their current context and practice.

In designing HEAR-MI Coaching, we centered EAR-MI because the rubrics reflect research-aligned equitable teaching practices. The practices included in the rubrics were also of an appropriate grain-size for a focus on smaller adjustments to practice rather than wholesale reform. Interviews with teachers suggest that the use of rubrics and their structure were an important feature of the model. Teacher participants noted that the rubrics provided a clear structure and guidance for instructional change, allowing them to make connections between their current approaches and clearly articulated adjustments they might make. Furthermore, the rubrics supported them to see these as practical and actionable. For example, one teacher stated, “seeing like examples that were provided in the rubric was kind of like, oh, okay, these are some things that I’ve—I’m already doing, but I could enhance it by adding more and enhance it by providing that rationale”.

In addition, participants noted that the EAR-MI rubrics supported shifts in teaching practice because they decomposed the focal teaching practices into their component parts and provided concrete guidance for enactment. For example, one teacher noted the specificity the rubrics provided around aspects of the teaching practices, sharing, “the rubrics [are helpful] because they, because of the examples of like what the teacher would say on a given level, I think all the times many rubrics are like, ‘teacher is supposed to give clear instructions’, but what is the clear instructions going to sound like?” Another teacher reflected on how understanding the specific aspects of the practice supported them to integrate the practice into their teaching:

When I was doing Math Expectations, there was a third part that talked about–what was it? I think it was like—[Interviewer: Rationale?] Right, right. Telling kids why that is important. A lot of the times when you when—when I’m teaching, I tend to forget that part, right? And that’s super important for the kids to know. So, so again, that rooted me back, like gave me that focus and that goal to try to meet it as much as I could. So that’s good. I think I did it—I did it, and I and I felt like—I felt that I—it was successful, and–and because I had that time to talk about it and, and practice it and hear my coach’s like feedback, I—I feel—I feel better now and more confident that I’m gonna use it next year more naturally, right, than I did this year.

In describing what they found useful about working their focal rubric (Math Expectations) one teacher described how the specific indicators of the practice (providing clear instructions, providing an image of productive participation, and providing a rationale for why the expectations are important) influenced an awareness that led to changes in their own practice:

I go day in, day out, teach these lessons, but I don’t always know if the students know, like what the punchline or what the goal of the day was, so the rubric, especially for the clear instructions, I think it made me very much aware that I need to at some point tell the students like why it’s important… So, being able to give them that at one point during our lesson, and then being able to give them those clear instructions and solidify everything at the end like this is what we did today, this is how it’s going to connect to tomorrow, or this is how it connected to yesterday, so that they get kinda like that flow going and seeing how every single lesson is not just, I’m going to learn it and forget it, because I got tested on it—that they are going to come back, and you know they all connect to each other.

A different teacher described how decomposing Math Expectations into its component parts and then discussing these with their coach supported them to reflect on and enhance existing practice:

Usually, I’m able to state the clear expectation of what I want them to do, and then, when it comes to the different ways of showing example or modeling of successful work, she gives me a lot of ideas on how I can enhance, maybe what I’m already doing. Let’s say I’m modeling, she could enhance it even more by showing like an anchor chart, or pointing to where the resource are, and just like simple things like that, but providing them with that choice of access point, and then the rationale, the rationale is where I struggle with the most, and being able to talk about it through every translation with her during the pre—in the beginning of the cycle, was really helpful.

Another teacher reflected that the small, meaningful changes suggested through aspects of one rubric practice supported her to consider incorporating other ways to make her instruction more equitable:

So, I actually had talked to my coach about, possibly like, now that we’ve talked about the clear instructions, maybe starting to think about where else we can include one of the other rubrics here on out… So now it’s like, how can you make [lessons] better each year? And how can you make those small changes to make the lessons just more impactful for the students?”

In this way, seeing the impact of small shifts from working on one of the rubrics opened up the possibility for additional changes tied to other rubrics.

Another element of HEAR-MI Coaching that supported incremental improvement was the use of predictable, structured routines in coaching conversations. The describe and elevate routine was designed to provide structure and accountability, focusing coaching conversations around specific teaching practices rather than allowing them to drift to other topics. Teachers identified aspects of the routine itself as facilitating adjustments to their teaching practice. For example, one teacher reflected on how video analysis—and specifically the use of the rubric and transcript annotations—supported her to envision small adjustments to her own practice:

That’s when it started getting a little, I guess interesting, seeing once we started the actual conversation, how I would place things specifically for the evidence. Like for the evidence I found myself kind of all over the place the first time, not really knowing well does it count for this? … Where would I place it? But it also made me aware of, like, you know when we—we added, like certain dialogue that you could have changed, like if we could have gone back and edit ourselves, how just one sentence could have made a huge difference in the rubric… I was able to comment directly on the transcript and then we went over that together. One of the things that I really liked is seeing how we could have edited the transcript, or essentially what I could have changed to get that to the next level. So, I really did like that because I felt like it made me realize this—how small changes could really essentially make the lesson better—like a lot better.

A different teacher reflected that using the rubrics to analyze video from our project library facilitated connections to their current practice, noting that “we’d look at like what they [the teacher in the video] did well, what could have been improved, and then see how that maybe connects to what I’m currently doing in the classroom”. For these teachers, using the transcript alongside the rubric during the elevate portion of the discussion was key to understanding how to deepen the rubric practice.

A key feature of incremental improvement approaches is that they build from teachers’ current practice. HEAR-MI Coaching was designed to incorporate self-directed learning and teachers identified choice and agency around goal-setting and rubric selection as supportive features for this building work. As part of the model, teachers determine their own goal for each coaching cycle and, with support from their coach, select a focal EAR-MI rubric that they feel aligns with their goals. Teachers described the selection of the focal rubric as a collaborative conversation with their coach rooted in their broader goals for their teaching. For example, according to one teacher,

It was a conversation. We kind of sat down, she had me read through all of them [the EAR-MI rubrics] and think of my own teaching and kind of like just my goals for the year. One of my goals is always just to talk less and have the students do more and so that just was aligned to that rubric [that I chose].

Another teacher aligned their choice of rubric to both their goals for their students and to their school’s broader goals:

I did have a very large [English Language Learner] group… So, I wanted to know how I could just—I wanted this, you know, feel for how I can easily make [math] accessible to the students… So [my coach]—she agreed that that was something that we needed to do. Our school is moving to more of a student-centered environment either way, so we felt that [Math Expectations] was one that aligned with our schools goals as well as my own.

The choice and agency afforded teachers to direct the focus of the coaching cycles allowed them to take ownership of the process. For example, one teacher reflected on how this feature supported buy-in:

[My coach] showed me the rubrics, and she said, you know, depending on—like depending on your own goals as a teacher, here’s some rubrics that we can look at and work on and so it was mainly my choice. So I got to choose the rubrics and the times that we switched rubrics was because I felt that—that I was already strong in that… I really like that she—she allowed me—she gave me a lot of choice, and because she gave me a lot of choice, I was more dedicated to meeting the rubric.

For this teacher, the ability to select rubrics, both initially and throughout the year, supported their enactment of the EAR-MI practices in their own teaching. Because the model allowed teachers to focus on one practice at a time, teachers were also able to determine when they felt ready to move on to another focal practice.

5. Discussion

Despite calls for mathematics instruction to be more ambitious, student-centered, and meaningful for students, large shifts in teaching practice have not taken root (Hiebert et al., 2005; Litke, 2020b). Similarly, we see minimal evidence that mathematics classrooms at scale support and affirm students from historically marginalized backgrounds and include equitable teaching practices (Boston & Wilhelm, 2017; Wilson et al., 2019). Professional learning that aims to shift teaching in ways that reflect large shifts from current practice may encounter challenges if teachers do not see those changes as practical, congruent with their context, or when perceived benefits outweigh the costs of reform efforts (Janssen et al., 2015). In contrast, incremental approaches to instructional improvement begin with current practice and seek to bridge toward larger shifts through the accumulation of smaller, meaningful changes to finer-grained aspects of teaching (Janssen et al., 2015; Litke, 2020a; Otten et al., 2022; Star, 2016). In this article, we shared how one professional learning model—HEAR-MI Coaching—was designed to encompass these features. Through understanding teachers’ experiences with the coaching model, we also identified additional features that supported teachers to shift their teaching toward practices that reflect more equitable mathematics classrooms.

Through its use of the EAR-MI, HEAR-MI Coaching focuses on a sub-set of research-aligned, equitable teaching practices (e.g., considering how to respond to students’ requests for assistance in ways that support mathematical agency) that are at a grain size suitable for small adjustments (Star, 2016). More ambitious or critical conceptualizations of equitable teaching (e.g., lessons that integrate math with social justice) may still be an end goal; however, they require extensive planning and knowledge to implement. Teaching practices such as those delineated by the EAR-MI may be less dependent on teachers developing specific critical or cultural knowledge or understanding, can be integrated into existing curricular expectations, and may require less buy-in from administration or district leaders. As such, they may have lower barriers to enactment and may be more immediately actionable.

While incremental improvement approaches to teacher professional learning may not always center frameworks such as EAR-MI, our experience suggests benefits to providing teachers with clear descriptors of teaching practices, delineating aspects of those practices, and providing guidance on enactment. Teachers who participated in HEAR-MI Coaching identified that the rubrics provided a level of specificity that supported them to enact small changes to their instruction. They highlighted how the rubrics’ descriptors of the components of each practice provided concrete guidance that facilitated uptake (de Araujo et al., 2022; Janssen et al., 2015). Furthermore, by articulating “good, better, and best” indicators of each practice (Kraft & Hill, 2020; Wilson et al., 2019), the rubrics also provided teachers with an image of successful enactment. Rubric indicators provided specificity that allowed teachers to envision small but meaningful shifts that they could then implement in their own classroom. In this way, the rubrics supported reflection on teaching by providing coaches and teachers both a shared language around equitable teaching and a focus for video analysis (Borko et al., 2008; Suh et al., 2021).

In addition, the routines and structures in HEAR-MI Coaching (e.g., goal setting, describe and elevate, action steps) provide a productive framework for coaches and teachers to engage in targeted discussions around teaching improvements geared toward enacting changes to practice. In particular, the predictable and repeated structure provided by the describe and elevate routine allowed for coaching conversations to go into greater depth (Horn & Little, 2010) and held coaches and teachers accountable for discussing specific teaching practices, rather than allowing conversations to drift to other topics. The use of video clips from our project library supported coaches and teachers to discuss a range of practices, depersonalize the analysis, and develop a shared understanding of what the EAR-MI practices look like. The use of video from the teacher’s classroom allowed for the application of the EAR-MI to teachers’ own context, supporting both self-reflection and instructional shifts. Teachers identified ways that the routine supported them to enact small adjustments to teaching (e.g., using transcript annotations to visualize what enactment could entail). These adjustments were then relatively easy to implement. Such modest instructional changes hold the potential to be sustainable and scalable (Otten et al., 2022). Those interested in developing professional learning focused on incremental improvement might consider how routines such as this can support teachers to envision, and ultimately enact, instructional shifts.

A key feature of incremental improvement approaches is that they meet teachers where they are, building on current practice. In HEAR-MI Coaching, while improvement goals and action steps are guided by the EAR-MI, they are chosen by the teacher to reflect their needs, contexts, and classroom realities. As adult learners, teachers benefit from a problem-centered approach to learning that leverages intrinsic motivation and is both applicable to their current context and immediately actionable (Knowles et al., 2012). Participating teachers noted the importance of setting their own improvement goals and choosing a focal rubric that aligned with those goals. Building teacher choice and agency into HEAR-MI Coaching therefore supported teachers to connect to and build from their current practice. Other approaches to professional learning focused on incremental improvement might consider how to foreground similar self-directed learning, as doing so has the potential to support buy-in and seed sustainability (Otten et al., 2022; Star, 2016).

We close by noting that coaching models such as HEAR-MI Coaching may be particularly suited for incremental approaches to developing more equitable teaching. The model leverages mathematics coaches as a catalyst for professional learning and incremental instructional change. Coaching is a form of job-embedded professional learning and coaches bring to their work with teachers situated, contextualized knowledge of teachers and schools (Marshall & Buenrostro, 2021). Coaches can provide individualized, sustained, and content-focused support that is job-embedded and rooted in teachers’ contexts (Kraft et al., 2018). Content-focused coaches can support teachers to develop their mathematics teaching through goal setting, evaluating teaching practice, locating teaching quality along a continuum, and identifying action steps (Gibbons & Cobb, 2016). In addition, coaching cycles leverage a pre-existing structure in schools (Otten et al., 2022). HEAR-MI Coaching cycles occurred during the time in which coaches and teachers already met with one another, shaping how that time was used but not layering on additional requirements. While organizational structures in schools and districts can obstruct large-scale instructional change (Star, 2016), coaches may be able to work within existing structures to support shifts in practice (Woulfin & Spitzer, 2024). Furthermore, coaching offers a potentially promising way to support teachers to enact more equitable teaching specifically, as coaches can leverage knowledge of equitable practices and relationships with teachers to encourage justice-oriented approaches to teaching (Marshall & Buenrostro, 2021).

It is important to consider whether incremental improvement approaches are appropriate for equity-oriented work. Otten et al. (2022) rightly ask, “Can deep systemic issues of inequity and injustice in mathematics education be meaningfully addressed in an incremental manner?” (p. 1448). However, we argue that smaller adjustments focused on equitable teaching practices may be a necessary first step in bridging between current practice and the types of teaching that will affirm students’ mathematical and cultural knowledge and identities. Star (2016) cautions that the focus of incremental improvement efforts should be chosen “for their potential to positively affect student learning while opening a door within teachers’ practice for more ambitious instructional changes in the future” (p. 59). Whether the accumulation of smaller-scale equity-focused practices will lead to more equitable classrooms remains an open question. Additional research is needed to understand whether and how models such as HEAR-MI Coaching can shift teachers’ beliefs and practice and support student outcomes. As part of our larger project, we aim to address questions such as this. Through an experimental study of HEAR-MI Coaching in two additional school districts, future research will explore the extent to which participation supported shifts in teachers’ beliefs and practice, student outcomes, and students’ sense of belonging in mathematics class. Further research is also needed to understand how to support teachers to bridge from the types of practices articulated in the EAR-MI to more “ambitious” teaching rooted in culturally sustaining or justice-oriented practices.

We do not advocate that professional development approaches abandon efforts at large scale changes to mathematics instruction focused on equitable, culturally sustaining and affirming, and justice-oriented teaching. However, given the complexity and difficulty of enacting large changes to teaching practice (Cohen, 2011), coaching efforts that focus on small shifts building on teachers’ extant practice to include facets of more equitable teaching may be an important start. Such efforts have the potential to impact how students experience mathematics in meaningful ways. Coaching models that aim to shift toward more equitable instruction in these ways should be intentionally designed to incorporate key features of incremental improvement that support teacher learning and practice.