## Details

Original language | English |
---|---|

Journal | ZDM - Mathematics Education |

Volume | 2024 |

Publication status | E-pub ahead of print - 13 Jul 2024 |

## Abstract

## Keywords

- Complex analysis, Complex path integrals, Commognition, Interpretations, Intuitive mathematical discourse, 97I80

## ASJC Scopus subject areas

- Social Sciences(all)
**Education****Mathematics(all)**

## Cite this

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**Experts’ intuitive mathematical discourses about integration in complex analysis.**/ Hanke, Erik.

In: ZDM - Mathematics Education, Vol. 2024, 13.07.2024.

Research output: Contribution to journal › Article › Research › peer review

*ZDM - Mathematics Education*, vol. 2024. https://doi.org/10.1007/s11858-024-01610-x

*ZDM - Mathematics Education*,

*2024*. Advance online publication. https://doi.org/10.1007/s11858-024-01610-x

}

TY - JOUR

T1 - Experts’ intuitive mathematical discourses about integration in complex analysis

AU - Hanke, Erik

N1 - Publisher Copyright: © The Author(s) 2024.

PY - 2024/7/13

Y1 - 2024/7/13

N2 - Although complex analysis is part of the study programs of many mathematics undergraduates, little research has been done on how individuals interpret basic concepts from complex analysis. To address this gap, this paper investigates how experts individually think about complex path integrals. For this purpose, the commognitive framework is used to conceptualize experts’ interpretations of mathematical concepts discursively, namely in terms of so-called intuitive mathematical discourses. A total of nine interpretations of complex path integrals, so-called discursive images, as well as eight sets of rules governing their construction, so-called discursive frames, are derived from expert interviews. These interpretations range from a rejection of intrinsic meaning to connections with real and vector analysis, mean values, and individual formulations of theorems. The paper also raises questions for the inclusion of the results into teaching and addresses further research.

AB - Although complex analysis is part of the study programs of many mathematics undergraduates, little research has been done on how individuals interpret basic concepts from complex analysis. To address this gap, this paper investigates how experts individually think about complex path integrals. For this purpose, the commognitive framework is used to conceptualize experts’ interpretations of mathematical concepts discursively, namely in terms of so-called intuitive mathematical discourses. A total of nine interpretations of complex path integrals, so-called discursive images, as well as eight sets of rules governing their construction, so-called discursive frames, are derived from expert interviews. These interpretations range from a rejection of intrinsic meaning to connections with real and vector analysis, mean values, and individual formulations of theorems. The paper also raises questions for the inclusion of the results into teaching and addresses further research.

KW - Complex analysis

KW - Complex path integrals

KW - Commognition

KW - Interpretations

KW - Intuitive mathematical discourse

KW - 97I80

UR - http://www.scopus.com/inward/record.url?scp=85198408479&partnerID=8YFLogxK

U2 - 10.1007/s11858-024-01610-x

DO - 10.1007/s11858-024-01610-x

M3 - Article

VL - 2024

JO - ZDM - Mathematics Education

JF - ZDM - Mathematics Education

SN - 1863-9690

ER -