PROCEEDINGS OF THE 20TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2017
San Diego, California
Completeness and convergence: Interdependent development in the context of proving the Intermediate Value Theorem
Page: 945
As a part of a larger RME-based instructional design project for advanced calculus, this paper reports on two students’ reinventions of formal conceptions of sequence convergence and the completeness property of the real numbers in the context of developing a proof of the Intermediate Value Theorem (IVT). Over the course of ten, hour-long sessions I worked with two students in a clinical setting, as these students collaborated on a sequence of tasks designed to support them in producing a proof of the IVT. Along the way, these students conjectured and developed a proof of the Monotone Convergence Theorem. Through this development I found that student conceptions of completeness were based on the geometric representation of the real numbers as a number line, and that the development of formal conceptions of sequence convergence and completeness were inextricably intertwined.