PROCEEDINGS OF THE 15TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION (Vol 2)
2012
Portland, Oregon
Definite Integral: A Starting Point for Reinventing Multiple Advanced Calculus Concepts
Page: 2-561
While recent Realistic Mathematics Education (RME) studies have shed light on students’ abilities to formalize limit conceptions, it remains to be seen how students might make similar progress with other fundamental advanced calculus concepts like continuity, derivative, and integral at a depth required for success in upper-division courses. To address this gap in the literature, we conducted a fourteen session teaching experiment geared at students’ reinvention of the formal definition of definite integral. Our presentation will address the following research questions: 1) Do students’ efforts to formalize the concept of definite integral motivate a need (for them) to formalize the notion of convergence/limit?; and, 2) Once students reinvent a formal definition of definite integral, can they use this formalization as a tool for formalizing other advanced calculus concepts? If so, which concepts?