ABSTRACT
In this chapter, we unpack what it means to know and learn mathematics well (or with understanding). We refer to mathematics knowing as five interconnected strands of proficiency outlined by the National Research Council and mathematics learning as the combination of three learner-driven processes (or mechanisms). We summarize the strands of proficiency, explicate the mechanisms that students use to advance their knowledge, present a case of one student to further explicate the mechanisms of student learning in the context of a supplemental mathematics intervention space, and provide connections between the mechanisms of student learning and teacher practice in supplemental intervention settings.
