PROCEEDINGS OF THE 19TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2016
Pittsburgh, Pennsylvania
IVT as a starting point for multiple real analysis topics
Page: 1305
In this paper I argue that the proof of the Intermediate Value Theorem (IVT) provides a rich and approachable context for motivating many concepts central to real analysis, such as: sequence and function convergence, completeness of the real numbers, and continuity. As a part of the development of a local instructional theory, an RME-based design experiment was conducted in which two post-calculus undergraduate students developed techniques to approximate the root of a polynomial. They then adapted those techniques into a (rough) proof of the IVT.