PROCEEDINGS OF THE 23RD ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2020
Boston, Massachusetts
Investigating student reasoning about the Cauchy-Riemann equations and the amplitwist
Page: 1179
Students appear to experience difficulty in coordinating different types of reasoning and different types of representations. Furthermore, they appear to start integrating these different modes of reasoning or representations when prompted to embody a given abstract mathematical concept. This research is part of an ongoing investigation into how students reason geometrically about various aspects of complex numbers, such as derivatives of complex-valued functions or the Cauchy-Riemann equations (hereafter the CR equations). Collection and analysis of the data is ongoing but is hoped to produce potential learning trajectories or natural ways in which students reason about the CR equations and their connections to the derivative.