Research has shown the majority of students who have completed a university calculus course reason about the definite integral primarily in terms of prototypical imagery or in purely algorithmic and non-quantitative ways. This dissertation draws on the framework of Emergent Quantitative Models to identify how calculus students might develop a…

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…