How does flexible mathematical thinking contribute to the growth of understanding?

Abstract

We examine aspects of flexible mathematical thinking in middle school students and its contribution to the growth of their mathematical understanding. We inductively analyzed data collected from video-episodes of an interactive, problem-solving based after-school mathematics class. Flexibility is essential in such classrooms since students must apply knowledge rather than simply retrieve it in its original context. The study provides links between flexibility and an existing theory of mathematical development to give researchers and teachers a better theoretical grasp of what happens in interactive classrooms.