This report is focused on what research and practice indicate about how assessment impacts the teaching and learning of STEM subject matter in K-12 classrooms. The intent is to take stock of what is currently known as well as what needs to be known to make classroom assessment in STEM maximally beneficial for the instructional practices of teachers and the learning outcomes of students. The volume draws inspiration from the cumulative body of research on STEM education that has accrued over the last two decades. The major sections in this report, individually and collectively, focus on critical issues regarding assessment integration and use at the classroom level. [For the executive summary, see ED631657. For the recommendations, see ED631658.]