The landscape of mathematics education research is undergoing a crucial shift, with equity taking center stage. Simultaneously, there is an increased need for relevant professional development to support math educators in light of this shift, to ensure equitable mathematics instruction for all students, but especially those who have been historically marginalized. Where much of the attention for this work has been placed on teachers (Hopkins et al., 2017), we recognize that instructional leadership is a partnership between those that deliver the instruction (teachers) and those that support them in this work (instructional coaches). Asset-oriented frameworks such as rehumanizing mathematics (Gutiérrez, 2018) and ambitious and equitable mathematics (Chen & Horn, 2022) have helped researchers focus on teachers, but frameworks centered on coaching for equity are noticeably lacking (Marshall & Buenrosto, 2021) . A cursory scan of coaching research informs us that there is no standardized entry into mathematics coaching (Hannan & Russell, 2020; Russell et al. 2020), and with this, no uniform way to orient coaches to their role within various contexts (e.g. Bengo, 2016; Gibbons et al., 2017; Russell et al., 2020) and no uniform preparation for coaches on how to support teachers in equitable mathematics teaching, particularly when the teacher demonstrates traditional or marginalizing views. Mathematics coaching activities, such as co-teaching, modeling instruction, and structured coaching cycles can effectively support teachers' growth in instructional practices (Gibbons & Cobb, 2017; Russell et al., 2020), but a teacher’s asset-based orientation is the necessary fertile soil to cultivate truly inclusive mathematics classrooms.

This means that a vital role of equitable math coaches is recognizing and supporting/addressing deficit dispositions of the teachers they support. For example, deficit dispositions are demonstrated when a teacher opts for strategies that emphasize knowledge transmission (e.g. direct instruction, memorization, repetition, etc.) rather than those that encourage interaction with rich mathematical content depth of knowledge (Pringle et al., 2012). Schools use mathematics coaching as a form of professional development for mathematics teachers (Kazemi et al., 2016; Russell et al., 2020). Mathematics coaches also need professional development to support their work of problematizing deficit orientations (Marshall & Buenrostro, 2021). Coaching in this context may involve critical conversations and/or activities that do not happen with enough frequency for coaches to develop skills and strategies for equitable coaching. Digital simulations, however, could be the innovative practice space that is needed.

Digital Simulations as Practice Spaces

Digital Simulations are an increasingly popular tool that can provide coaches the opportunity to distill the complex task of instructional coaching into smaller, distinct, manageable approximations without people present (Hillaire et al., 2022). Digital simulations also assure a safe space to practice instructional coaching without the full complexity of the position, cultivating an environment for risk-taking, learning, and unlearning (Grossman et. al, 2009). In particular, our design featured Teacher Moments (teachermoments.mit.edu), a digital clinical simulation platform that uses prompts, images and videos as a way to immerse users in the complexities of the teaching/coaching practice.

Simulation Design

This article leverages data from Case Study: Coaching Mr. Dailey, a simulation inspired by a real-life coaching experience faced by one of our coaches. Specifically, coaches engaged in a simulation featuring a fictional character, Mr. Dailey, a 10-year veteran who teaches 7th grade and holds deficit perspectives about his students, reflected in his use of mathematics problems that take a short time to solve and his belief that math problems must be solved in predetermined ways. These beliefs reveal low expectations of the students. This particular coaching experience was aimed at coaches of math teachers in schools with large (more than 90%) populations of students of color, schools typically classified as urban (Milner, 2012). While digital simulations can benefit math coaches of teachers in a variety of environments, deficit dispositions are prevalent in urban schools, elevating the potential for harm (Davis & Martin, 2008; Reyna, 2000). During the simulation (see Figure 1) Mr. Dailey functions as a lecturer, looking strictly for correct algorithmic answers. Throughout the simulation, he tells students what to do, making no space for their thinking and consistently positions students as observers (not contributors) to their mathematical experience.  

As part of the simulation's dynamics, participants were presented with a notepad as an opportunity to record notes as they progressed through the scenario, mirroring one of the responsibilities of an instructional coach.

​​Figure 1^[1]

Enact 2 within Mr. Dailey Simulation

After three scenes of problematic teaching by Mr. Dailey, participants were instructed to engage in a simulated debrief conversation with him. Here, instructional coaches got the opportunity to revisit their notepads and identify a productive instructional goal for Mr. Dailey. However, Mr. Dailey was designed to resist any recommendations expressed by the coaches (Figure 2).

Figure 2

Further he makes his deficit framing clear as he states:

Listen, I've been doing this for 10 years. Some students are in LALA land and just don't get it unless you show them one way to do it and give them an opportunity to practice it 100 times. That is why I said we should work on the exit ticket because I want to see if they are using the way I showed them.

This moment was designed to surface the coaches’ “in-the-moment” responses to a teacher's deficit lens. What follows is how we analyzed the coaches’ response to Mr. Dailey’s deficit orientation.

Preliminary Findings

As one might imagine, there were a multitude of ways to analyze and interpret the responses from the coaches in the simulation, with each possibility revealing more insights and questions. What we chose to share in this article was a finding with possible implications for both early career and experienced coaches. In the first layer of analyzing the responses of the coaches in the study, we focused our attention on whether each coach accepted, ignored, or challenged Mr. Dailey’s statements. In the second layer of analysis, we attended to what was accepted, challenged or ignored - was it Mr. Dailey’s disposition or his choice of pedagogical tool? For the sake of consistency, statements that we coded as “accept” or “challenge” needed to refer to something Mr. Dailey says in his remarks i.e. an “accept” can be as simple as an acknowledgement, and a “challenge” can be a question or a rebuttal. We categorized “ignore” as statements that do not mention or refer to specific issues of disposition or pedagogy. Please remember that this exercise was not intended to punish or point fingers at any coach; our goal at this point in the analysis was to first notice any patterns that emerge in what is accepted, challenged or ignored. Ultimately, this experience should enable open discussions that lead to the sharing of resources and strategies when coaching a teacher who openly displays damaging dispositions towards urban students.

Below (Figure 3), we share the responses of two coaches from the study: Coach VC and Coach ECC.

Figure 3:  Comparison of Responses from Coach VC and Coach ECC

In Coach VC’s response, we first see a challenge to Mr. Dailey’s statement about students being in “la-la land”, followed by a challenge to Mr. Dailey’s pedagogical choices through Coach VC’s questions about “the purpose of cognitively demanding tasks”. There was an acceptance of the pedagogical tool at the end of the response, which was then followed by a wish to “spend time unpacking that”, but the previous statement is a challenge to the intended use of the pedagogical tool. In contrast, Coach ECC ignores Mr. Dailey’s disposition by making no mention of it, and then accepts Mr. Dailey’s selection and use of the pedagogical tool by saying “let's go ahead and take a look at the exit tickets...and see if we think students are understanding [pause] what we want them to learn”. We should note that Coach VC had 10 years of experience in this coaching role whereas Coach ECC had been in the position for only 1 year at the time of the study.

This early finding illuminated how often Mr. Dailey’s troubling disposition was ignored. Most of the coaches in the study (9 out of 10) ignored the “la-la land” comment that Mr. Dailey made about the students, and we saw that most statements coded as “challenge” were a challenge to the intended use of the pedagogical tool. The coaches focused their responses to issues of pedagogy, whether the pedagogical tool was suitable to the task of determining student learning, or whether the intended use of the pedagogical tool would accomplish Mr. Dailey’s goal.

Discussion and Key Takeaways

In the findings from the initial layers of analysis, we drew attention to the participants’ years of experience because we noticed that there appeared to be a slight correlation between the years of experience and the comfort and skill in challenging Mr. Dailey’s pedagogical choices. Coaches with more experience demonstrated more finesse in framing their challenge without appearing confrontational. We did not see a similar relationship in who did and did not challenge Mr. Dailey’s disposition. In fact, what was remarkable was how common it was among the coaches who had different years of experience and different paths of entry into the coaching role. We acknowledge that the lack of coaching experience could have made the task of confronting a teacher like Mr. Dailey seem daunting. We also acknowledge that the limited training on the specific coaching needs for teachers in urban math classrooms could make coaches, irrespective of experience, feel unprepared and uncomfortable challenging a teacher like Mr. Dailey.  However, the cost of not addressing the Mr. Dailey’s in urban math classrooms is too great to overlook.

Next steps/Future research/Conclusion

Our purpose in this article was to offer an example of how digital simulations can support the professional development needs of math coaches. The findings from the digital simulation experience of the coaches in this study offered insight into what professional development and resources math educators, math coaches, and teacher educators might need to create fertile ground for equitable math instruction. District leaders and administrators might also consider the implications of these findings and the corresponding need for the establishment of protocols and procedures to support equitable instructional practices at a system level (Hopkins et al., 2017). Because coaches work with teachers in specific local contexts, any interventions will also need to be localized to be impactful (Adler, 1982; Ladson-Billings, 2014; Marshall & Buenrostro, 2021). The research team in the study will extend the study to include reflections for insight into the coaches’ decision-making process as they crafted their response to Mr. Dailey.

The ultimate goal of the coach/math teacher interaction is to ensure that coaches of math teachers feel supported enough to intervene when inequitable math teaching practices are being enacted. Digital simulations can offer insight to specific pedagogical issues exhibited by instructional staff (teachers and instructional coaches), which can be used to craft interventions or curating resources to support their professional growth.

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