The information that is most valuable for teaching must focus on student thinking. Dylan Wiliam states that, "The central idea of formative assessment, or assessment for learning, is that evidence of student learning is used to adjust instruction to better meet student learning needs." He describes formative assessment practice as students and teachers using evidence of learning to adapt teaching and learning to meet immediate learning needs, minute-to-minute and day-by-day (>>more). Most teachers don't actively use these practices, in part because few teachers are trained to use formative assessment and have no apprenticeship implementing its use in classrooms.
Quality math performance assessments, coupled with effective professional development for classroom teachers and leaders, can support improved instruction and student achievement. Teachers need in-depth understanding of mathematical concepts and effective strategies for instruction. Without these in-depth understandings, it is challenging to design instructional experiences that drive significant student achievement. Teachers can improve instructional effectiveness by using a cycle of formative assessment practice. As they examine the student thinking revealed in the assessments and consider each student's current knowledge and misconceptions, teachers also clarify and strengthen their own understanding of mathematical concepts.