# Jon Star – New directions in the study of (and assessment of) mathematical flexibility

In this talk, I reflect on procedural flexibility and how it can be measured and studied. I draw upon my own definition of procedural flexibility, where I define flexibility to be knowledge of multiple strategies and the ability to select the most appropriate strategy for a given problem and problem-solving circumstance. I begin with the premise that in order to study flexibility, we must have reliable ways to measure it. It follows then that to measure flexibility, we need to come to terms with two challenging definitional issues related to the construct. The first of these – the “different question” – concerns what it means for one strategy to be different than another. The second issue – the “best question” – is about what it means for one strategy to be better or more appropriate than another. I then discuss ways that researchers in the field have been and are thinking about how to assess procedural flexibility, and I consider how these methods of assessment implicitly and explicitly provide answers to the “different question” and the “best question.”