## Details

Original language | English |
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Title of host publication | INDRUM 2022 PROCEEDINGS: Fourth conference of the International Network for Didactic Research in University Mathematics |

Editors | María Trigueros, Berta Barquero, Reinhard Hochmuth, Jana Peters |

Pages | 164-173 |

Publication status | Published - 2022 |

Event | Fourth conference of the International Network for Didactic Research in University Mathematics - Hannover, Germany Duration: 19 Oct 2022 → 22 Oct 2022 Conference number: 4 |

## Publication series

Name | International network for didactic research in university mathematics |
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ISSN (Print) | 2496-1027 |

## Abstract

## Cite this

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**Vertical coherence in the teaching of integrals? An example from complex analysis.**/ Hanke, Erik.

INDRUM 2022 PROCEEDINGS: Fourth conference of the International Network for Didactic Research in University Mathematics. ed. / María Trigueros; Berta Barquero; Reinhard Hochmuth; Jana Peters. 2022. p. 164-173 (International network for didactic research in university mathematics).

Research output: Chapter in book/report/conference proceeding › Conference contribution › Research

*INDRUM 2022 PROCEEDINGS: Fourth conference of the International Network for Didactic Research in University Mathematics.*International network for didactic research in university mathematics, pp. 164-173, Fourth conference of the International Network for Didactic Research in University Mathematics, Hannover, Lower Saxony, Germany, 19 Oct 2022.

*INDRUM 2022 PROCEEDINGS: Fourth conference of the International Network for Didactic Research in University Mathematics*(pp. 164-173). (International network for didactic research in university mathematics).

}

TY - GEN

T1 - Vertical coherence in the teaching of integrals? An example from complex analysis

AU - Hanke, Erik

N1 - Conference code: 4

PY - 2022

Y1 - 2022

N2 - 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.

AB - 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.

UR - https://indrum2022.sciencesconf.org/data/Proceedings_Indrum2022.pdf

M3 - Conference contribution

T3 - International network for didactic research in university mathematics

SP - 164

EP - 173

BT - INDRUM 2022 PROCEEDINGS: Fourth conference of the International Network for Didactic Research in University Mathematics

A2 - Trigueros, María

A2 - Barquero, Berta

A2 - Hochmuth, Reinhard

A2 - Peters, Jana

T2 - Fourth conference of the International Network for Didactic Research in University Mathematics

Y2 - 19 October 2022 through 22 October 2022

ER -