Using Learning Trajectories to Enhance Formative Assessment
Numerous research studies have shown that formative assessment is a classroom practice that when carried out effectively can improve student learning (Black and Wiliam 1998). Formative assessment is not just giving tests and quizzes more frequently. When assessment is truly formative, the evidence that is generated is interpreted by the teacher and the student and then used to make adjustments in the teaching and learning process. In other words, the formative assessment generates feedback, and that feedback is used to enhance student learning. Formative assessment is therefore fundamentally an interpretive process: It is less about the structure, format, or timing of the assessment and more about the function and use by both the teacher and student (Wiliam 2011). For teachers of mathematics, the heart of this process is making sense of and understanding student thinking in relation to content goals.