Topological Structures for Exploring University Students’ Calculus Conceptions

Abstract

Calculus 1 is a major obstacle for students pursuing a degree in Science, Technology, Engineering, and Mathematics (STEM) at universities in the United States. This dissertation offers three studies on the student experience in calculus. I explore students’ mindsets during Calculus 1, students’ engagement with productive struggle during Calculus 1, and student understanding of the derivative during Calculus 1 and Calculus 3. This exploration is done from the perspective that Mathematics and Research in Undergraduate Mathematics Education (RUME) are two communities that are inextricably linked. Nevertheless, crossing from one community into the other requires expertise in both. Thus, I utilize methodologies from both fields, qualitative coding from RUME and topological approaches from mathematics. This dissertation presents the results of projects that exemplify an effort to cross the disciplinary boundaries of mathematics and RUME in order to become a broker and augment the methods in RUME with novel mathematical ones.