The commitment of resources to coaching almost always occurs in interaction with other district-wide efforts to improve instruction. Given this probable situation, it’s concerning that the field lacks the ability to provide guidance regarding how coaches might reasonably be integrated within overall plans for the coordination and improvement of instruction. Indeed, the field lacks a robust understanding of coaching beyond a siloed- endeavor or theories of coaching as one aspect of a district’s broader system for instructional improvement (i.e., the educational infrastructure). 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 dissertation, I examine and articulate relations between infrastructure for elementary mathematics and mathematics coaching. To do this, I utilize a cross-case analysis of two school districts with different infrastructure designs for elementary mathematics. I then surface similarities and differences between coaching practice in each district and show how they are related to key variations in the districts’ infrastructure within which these coaches work. More specifically, this dissertation addresses three questions: 1) What is the design of infrastructures for elementary mathematics in two school districts? 2) How do coaches enact their role in these different infrastructure designs? 3) How do variations in district infrastructures for elementary mathematics shape coaching practice?
I show 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 as they endeavored to improve elementary mathematics teaching. These designed infrastructures included formal role groups that were designed to engage in issues of instructional improvement, resources designed to “carry” the district vision to various communities across the district such as instructional materials and assessments, and designed participation structures for various role groups to participate in to learn about the district vision for mathematics teaching and learning. Coaches were a key component in both districts’ infrastructures.
While the two infrastructures had similar component parts, I show that the districts made different strategic choices regarding 1) who was connected through designed participation structures, 2) how clear and detailed the designed resources were, 3) the extent to which there were designed mechanisms to encourage adherence to the vision espoused in the infrastructure, and 4) the extent to which all the infrastructure components cohered around the adopted vision for mathematics teaching and learning.
Further, I show that while math coaches in both districts engaged in several common tasks, including planning and facilitating teacher professional learning, observing and debriefing teachers’ instruction, and building district level capacity, among others, 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. I show that these differences were related to the differences in the broader infrastructures within which coaches worked. For example, I found that the degree to which the design of the coaching role was integrated with other levers for improvement, joined with an overall press for the vision of mathematics infrastructure espoused in the infrastructure, shaped the relative balance in time coaches spent on various coaching tasks. In this way, I show how infrastructure design shaped lived coaching practice.
By broadening our notion of coaching practice beyond the individual coach and their knowledge, beliefs, and actions, this dissertation 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.