Even seemingly straightforward education policy ideas are interpreted and implemented quite differently as they make their way through the levels of the education system (Cohen, 1990; Cohen & Hill, 2001; Spillane, 2000). Complex ideas that lack clear and specific instructional guidance, like the Common Core State Standards in mathematics (CCSS-M) -- with their increased emphasis on rigorous and coherent content, standards for mathematical practice, and instructional pedagogies that support students' deep conceptual mathematics learning -- may prove challenging as teachers attempt to interpret and implement them in their own classrooms. The combination of limited instructional guidance for the CCSS-M and individual teacher variation (resulting from each teacher's different beliefs, skills, knowledge, and interests) leaves room for significant variation in how the central CCSS-M reform ideas are interpreted and implemented in the classroom. As such, there will likely be wide variation in teachers' instruction as they implement the CCSS-M in their classrooms.Yet if, as research has shown, teachers affect student achievement more than any other school-related factor (Rivkin, Hanushek, & Kain, 2005), Math in Common districts will need to understand and monitor how CCSS-M ideas are taught in classrooms in order to improve mathematics education for all students. Understanding the extent of teachers' instructional variation will help districts build on and spread best practices and support improvement of CCSS-M implementation
