Our purpose in this article is to propose a comprehensive, empirically grounded theory of action for improving the quality of mathematics teaching at scale. In doing so, we summarise current research findings that can inform efforts to improve the quality of mathematics instruction on a large scale, and identify questions that are yet to be addressed. We draw on an ongoing collaboration with mathematics teachers, school leaders, and district leaders in four urban school districts in the US. The provisional theory of action that we report encompasses a coherent system of supports for ambitious instruction that includes both formal and job-embedded teacher professional development, teacher networks, mathematics coaches' practices in providing job-embedded support for teachers' learning, school leaders' practices as instructional leaders in mathematics, and district leaders' practices in supporting the development of school-level capacity for instructional improvement. (Contains 1 footnote.)