Although there is no consensus in regard to a unique meaning for abstraction, there is a recognition of the existence of several theories of abstraction, and that the ability to abstract is imperative to learning and doing meaningful mathematics. The theory of "reducing abstraction" maps the abstract nature of mathematics to the nature…

The use of science classroom discourse analysis as a way to gain a better understanding of various student cognitive outcomes has a rich history in Science Education in general and Physics Education Research (PER) in particular. When students talk to each other in a collaborative peer instruction environment, such as in the CLASP classes…