PROCEEDINGS OF THE 22ND ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2019
Oklahoma City, Oklahoma
Distance measurement and reinventing the general metric function
Page: 492
Real analysis is an important course for both undergraduate and graduate students. Researching the ways students reason about challenging and abstract concepts can inform and improve instruction in real analysis. In this report, I examine two undergraduate students’ reinvention of a general metric function. To facilitate this reinvention, I conducted a 15-hour teaching experiment with undergraduate mathematics students that had completed the introductory sequence in real analysis. In this experiment, the students generalized their initial understandings of distance measurements on R to construct increasingly abstract measures of distance in various metric spaces, including sequence and function spaces. Their generalizing activity culminated in construction of a general metric function through reflected abstraction of operations relevant to distance measurement carried out in previous metric spaces. I explore the students’ generalizing activity, as well as the abstractions that supported their generalizing1.