The Relationship Between Mathematics Coaching and Broader Systems for Instructional Improvement in Two School Districts

• In Event: Understanding the Complexities of Mathematics Coaching: What Multiple Theoretical and Analytical Frameworks Reveal

Abstract

Coaching occurs in interaction with other district-wide efforts to improve instruction (Cobb & Jackson, 2011); however, the field lacks understanding of coaching beyond a siloed endeavor or theories of coaching as one component of a district’s educational infrastructure (Neumerski, 2012). Infrastructure refers to “the coordinated roles, structures, and resources that school systems design and use to support and coordinate instruction, maintain instructional quality, and enable instructional improvement” (Cohen, Spillane, & Peurach, 2018, p. 205). In this paper, we articulate relations between infrastructures for elementary mathematics and coaching practice in two school districts. To do this we drew on district and school leader interviews and artifacts as well as observations and interviews of coaches from two California districts during the 2018-19 school year. We utilized a cross-case analysis wherein we surfaced similarities and differences between coaching practice in each district and showed how they were related to key variations in the infrastructures within which these coaches worked.

We viewed coaching as a distributed practice (Spillane & Diamond, 2007). In this perspective, coaches’ interactions, as opposed to their actions, are foregrounded (Spillane, 2006). It also draws attention to the situation (persistent tools, artifacts, resources, and organizational structures that “stretch over” multiple activities) as a constituting element of coaches’ interactions (Spillane Halverson, & Diamond, 2001, p. 23). We treated district-designed infrastructures for elementary mathematics as the situation. Infrastructures, by their very nature, are persistent because they are designed to travel time and space (e.g., curricular frameworks) (Wenger, 1998, p. 179). Therefore, the distributed perspective suggests that coaching emerges as coaches—in interactions with others—use, enact, or co-perform different infrastructure components.

We found that both districts adopted similar visions for students’ mathematical learning and instruction. To achieve these visions, both districts designed infrastructure to guide and support school leaders and teachers. The infrastructures had similar component parts (including coaches), but we show that the districts made different strategic choices regarding 1) who was connected through organizational routines, 2) how clear and detailed the resources were, 3) the extent to which there were mechanisms to encourage adherence to the vision espoused in the infrastructure, and 4) the extent to which all infrastructure components cohered around the vision for mathematics teaching and learning. Further, we found that while mathematics coaches in both districts engaged in several common tasks (e.g., facilitating teacher professional learning, observing and debriefing teachers’ instruction), their enactments were different in several consequential ways, including how they divided time among various tasks, who they co-enacted tasks with, what resources they used and how, and the focus of their interactions. We showed that these differences were related to the differences in the broader infrastructures within which coaches worked.

By broadening our notion of coaching beyond the individual coach (and their knowledge, beliefs, and actions), this paper contributes to understandings of how coaching is couched within and interacts with the larger instructional improvement system. It also uncovers opportunities for intervention for those designing infrastructure to support the implementation of ambitious instructional reform in mathematics.

Authors

• Abigail Stein, Carnegie Mellon University
  Presenting Author

• Cynthia E. Coburn, Northwestern University
  Presenting Author