PROCEEDINGS OF THE 17TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2014
Denver, Colorado
Geometric Reasoning on the complex plane
Page: 1044
Using Bakker and Hoffman’s (2005) framework on diagrammatic reasoning, we analyzed a video-taped interview to explore two undergraduates’ ability to reason geometrically about tasks related to complex variables. Our findings indicate that in order to provide a geometric interpretation, our participants needed to first perform algebraic computations that reduced the current task to a task they knew how to interpret geometrically. These computations appeared to provide them with the pieces required to construct a diagram. Once these pieces were in place the participants used dynamic gesture to enact their geometric interpretations with the aid of their diagram. It appeared that their dynamic gestures assisted with embodying geometric interpretations and as such one particular task was influential throughout the interview. Furthermore, the participants integrated less dynamic gesture as they progressed with similar tasks.