Vertical coherence in the teaching of integrals? An example from complex analysis

authored by

Erik Hanke

Abstract

Students encounter integrals in a wide range of mathematical domains, often in relation to the ideas of measuring and mean values. Using the integral as an example, this paper discusses one aspect of the teaching and learning of advanced mathematics, namely, the use of core ideas of mathematical concepts to establish vertical coherence between mathematical domains in teaching. It will be explained to what extent the ideas of measuring and mean values can be used for complex path integrals. Then, the epistemological considerations in this paper are enhanced with a case from an expert interview. This case exemplifies the application of the two aforementioned ideas to complex path integrals, but it also points to a potential overgeneralisation from real to complex analysis.

Organisation(s)

Institute of the Teaching of Mathematics and Physics

External Organisation(s)

TH Köln - University of Applied Sciences

Type

Conference contribution

Pages

164-173

Publication date

2022

Publication status

Published