January 1, 2019
Although mathematics standards have changed dramatically in recent years, teaching mathematics is as complex as it has always been. Some would argue that mathematics teaching has become even more complex, with the implementation of the Common Core State Standards for Mathematics (CCSS-M) (NGA Center & CCSSO, 2010), as teachers are being asked to make significant shifts in their instruction.1 Teachers report that they are incorporating math standards into their daily practice and are feeling positive about their efforts to do so (Reade, Perry, & Heredia, 2018; Perry, Marple, & Reade, 2017), but the education field still has little empirical documentation on exactly how math teachers are shifting their classroom instruction to align with the CCSS-M. Exactly what are math teachers doing in their classrooms to help students master the standards?Part of the reason for the lack of data is the challenge of accurately measuring what happens during classroom instruction. The only real way to know what is happening in classrooms is through direct observation, and while it may be possible to get the gist of math classes through quick "drop-in" observations, it is ideal, for a systemic understanding of change, to use a valid and reliable observation instrument tied to specific elements of instruction. This sort of targeted instrument enables observers to obtain meaningful data and identify patterns in instruction across different lessons and teachers.Regardless of who carries out these observations and analyzes the resulting data -- teachers, principals, district staff, or partners from a research institution -- it is challenging and time-consuming work. But this work is essential in order to gain knowledge of how the standards are being implemented in classrooms to support all students in achieving mastery of the CCSS-M. Without understanding of how teachers and students are responding to the standards, it is impossible to know what supports and course changes are still needed, from either a district perspective or a policy perspective. Additionally, we frequently hear that there are not enough real-life examples of what the CCSS-M look like in classrooms when implemented well. Without examples of high-quality, standards-aligned instruction, it is difficult for educators to imagine how the standards should look and feel in their own classrooms, or to gauge their own progress. Carefully documented classroom observations can be a source of these sorts of real-world examples of standards-aligned instruction.The Math in Common (MiC) initiative was launched to support CCSS-M implementation in grades K-8 in 10 California school districts. As part of its evaluation of MiC, WestEd conducted classroom observations in participating MiC districts to document K-8 teachers' instructional shifts related to the CCSS-M. The research staff visited elementary and middle school classrooms in nine MiC school districts, during the 2015-16, 2016-17, and 2017-18 academic years, to observe and analyze mathematics lessons, using an observation protocol adapted for this project. Participants from MiC teams often joined us during the observations and debriefed with us afterwards.Our preliminary learning from these classroom observation data was publicly reported in a blog post characterizing common structural features of highly rated lessons (Seago & Perry, 2017) and in case studies of incremental change in teacher practice over time (Seago & Carroll, 2018). This report describes additional analyses of observation data on eight dimensions of classroom mathematics instruction. These analyses are drawn from our complete set of classroom observation data: 201 lesson observations, representing more than 130 hours of observation over three years. We begin the report by describing our classroom observation protocol and the dimensions of classroom instruction that we observed using this protocol. We then present our findings on the instructional variability that we saw across classrooms and districts. Next, drawing on classroom transcripts and observation data, we discuss what highly rated classrooms looked like across the various dimensions that we observed, and how administrators and others can support this sort of CCSS-M-aligned instruction. The report concludes with several recommendations for conducting effective classroom observations.Our primary goal with this report is to share with teachers and administrators what we have learned about how particular elements of CCSS-M-aligned instruction look and feel when implemented effectively in the classroom. We also wish to stimulate discussion in the field about what kinds of information can best help educators understand standards implementation, and to share emerging insights from our experience trying to measure shifts in mathematics instruction.