Teacher learning is a huge challenge in instructional change, but relatively little work has carefully examined the mechanisms by which teachers learn, in contrast to the extensive work on programs that help teachers learn and the high-leverage instructional practices that are strong predictors of student learning. Specifically, relatively little is known about how teachers learn to effectively implement these new instructional practices. Using a mixed-methods, case-comparison design, this study examines specific instructional coaching practices that support 4th-8th grade mathematics teachers in learning to implement ambitious instructional practices. The study leverages a large, state-wide representative dataset in order to purposively select carefully-matched contrasting cases for qualitative analysis from a starting sample of hundreds of teachers, which enabled selecting teachers that began in a very similar place but then progressed at different rates. In-depth qualitative coding was systematically conducted on detailed transcripts of coach-teacher conversations from these carefully selected cases. Finally, these codes were analyzed quantitatively to determine whether the content and form of these conversations predicted improvement in teachers' instructional practices. Results showed that coach-teacher pairs who discuss when and why certain practices should be implemented, and provide more opportunities for teacher input, see larger gains in ambitious instruction in later lessons. Implications for a coaching model based in the cognitive sciences are discussed.