Our purpose in this chapter is to propose that the concept of reflective abstraction can be a powerful tool in the study of advanced mathematical thinking, that it can provide a theoretical basis that supports and contributes to our understanding of what this thinking is and how we can help students develop the ability to engage in it. To make such a case completely, it would be necessary to do at least several things:• explain exactly what we mean by reflective abstraction;• show how it can be used to describe the epistemology of various mathematics concepts;• indicate how it can suggest explanations of some of the difficulties that students have with many of these concepts; and• establish that it can influence the design of instruction in ways that result in a significant improvement in th extent to which students appear to acquire these concepts.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.