PROCEEDINGS OF THE 20TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2017
San Diego, California
Undergraduates’ reasoning about integration of complex functions within three worlds of mathematics
Page: 1231
Recent research illustrates the importance of studying students’ nuanced mathematicalargumentation, as well as students’ tendency to invoke attributes of real numbers that no longerapply to situations in complex analysis. This preliminary report explicates a study exploringundergraduate student pairs’ reasoning about integration of complex functions. I amparticularly interested in students’ attention to the idiosyncratic hypotheses of powerfulintegration theorems as they evaluate integrals. Here reasoning is treated as contributing tocollective argumentation within one or more of Tall’s (2013) three worlds of mathematics. Datawere collected via task-based, semistructured interviews with pairs of undergraduates to elicitsuch reasoning, and classroom observations of the six class sessions devoted to integration priorto the interviews. All interviews have been transcribed and current analysis consists ofconducting a Toulmin (2003) analysis, augmented by a three-world classification. Potentialimplications of this work and connections to the associated literature are also discussed.