Instructional coaching has become a common practice internationally as a form of high-quality professional development for teachers (Desimone & Pak, 2017). Beyond the literature on mentoring and inducting pre-service and beginning mathematics teachers, instructional coaching for in-service teachers has been shown to be a valuable vehicle for diffusing innovative teaching practices and instructional reform (Hopkins et al., 2017). Thus far, research on coaching in-service mathematics teachers has focused largely on its effects on improving teachers’ practice and student achievement (Panfilio-Padden et al., 2025). But what makes for effective coaching, and what does it look like during instruction? Studies have aimed to distil the knowledge domains involved in coaching expertise, the nature of professional development for instructional coaches, and the wider contextual factors that may influence the dialogue that occurs between coaches and teachers (e.g., Saclarides & Kane, 2021; Sutton et al., 2011). A significant proportion of this research draws on the dialogue during the co-planning of a lesson and post-lesson reflections, which are often conducted as interviews or focus groups and typically involve observing recordings of teaching (e.g., Gillespie & Amador, 2024). However, less has been reported on the coaching dialogue that occurs in-the-moment during a lesson, which is arguably the most critical stage of the coaching cycle that has a direct impact on the learning opportunities available for both students and teachers.
In this presentation, we discuss illustrations of mathematics instructional coaches’ practices through the lens of routine and adaptive expertise (Anthony et al., 2015) to unpack what makes for effective mathematics coaching. We focus on the nature of the coaching dialogue, including how coaches and teachers attend to and reflect on students’ mathematical thinking, and how coaches initiate dialogue that contributes to effectively building trust and rapport for genuine co-construction of the lesson.