On using a core idea to foster the transition to advanced mathematics – transferring the idea of average to complex path integrals

Publikation: Beitrag in FachzeitschriftArtikelForschungPeer-Review

Autoren

Organisationseinheiten

Forschungs-netzwerk anzeigen

Details

OriginalspracheEnglisch
FachzeitschriftInternational Journal of Mathematical Education in Science and Technology
PublikationsstatusElektronisch veröffentlicht (E-Pub) - 7 Feb. 2024

Abstract

The transition from Riemann integrals to other real integrals has been discussed previously in mathematics education literature. In this transition, the interpretation of integrals as averages of the integrated functions generalises smoothly to measure and probability theory. In this paper, I address the transition to complex path integrals. Based on the premise that using core ideas throughout mathematics curricula may facilitate the transition from earlier to more advanced courses, I analyse epistemologically to what extent the idea of averaging may be transferred to complex path integrals. In this case, the transition poses special epistemological challenges. Using an example from an expert interview, in which the expert aims to apply the interpretation of integrals as averages to complex path integrals, I illustrate the aforementioned challenges empirically.

ASJC Scopus Sachgebiete

Zitieren

On using a core idea to foster the transition to advanced mathematics – transferring the idea of average to complex path integrals. / Hanke, Erik.
in: International Journal of Mathematical Education in Science and Technology, 07.02.2024.

Publikation: Beitrag in FachzeitschriftArtikelForschungPeer-Review

Hanke E. On using a core idea to foster the transition to advanced mathematics – transferring the idea of average to complex path integrals. International Journal of Mathematical Education in Science and Technology. 2024 Feb 7. Epub 2024 Feb 7. doi: 10.1080/0020739X.2024.2304882
Download
@article{fd9cb268b3f543d2bb8a9fd95ab4dc43,
title = "On using a core idea to foster the transition to advanced mathematics – transferring the idea of average to complex path integrals",
abstract = "The transition from Riemann integrals to other real integrals has been discussed previously in mathematics education literature. In this transition, the interpretation of integrals as averages of the integrated functions generalises smoothly to measure and probability theory. In this paper, I address the transition to complex path integrals. Based on the premise that using core ideas throughout mathematics curricula may facilitate the transition from earlier to more advanced courses, I analyse epistemologically to what extent the idea of averaging may be transferred to complex path integrals. In this case, the transition poses special epistemological challenges. Using an example from an expert interview, in which the expert aims to apply the interpretation of integrals as averages to complex path integrals, I illustrate the aforementioned challenges empirically.",
keywords = "Complex analysis, integrals, mean values, epistemology of mathematical objects, basic ideas",
author = "Erik Hanke",
note = "Publisher Copyright: {\textcopyright} 2024 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group.",
year = "2024",
month = feb,
day = "7",
doi = "10.1080/0020739X.2024.2304882",
language = "English",

}

Download

TY - JOUR

T1 - On using a core idea to foster the transition to advanced mathematics – transferring the idea of average to complex path integrals

AU - Hanke, Erik

N1 - Publisher Copyright: © 2024 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group.

PY - 2024/2/7

Y1 - 2024/2/7

N2 - The transition from Riemann integrals to other real integrals has been discussed previously in mathematics education literature. In this transition, the interpretation of integrals as averages of the integrated functions generalises smoothly to measure and probability theory. In this paper, I address the transition to complex path integrals. Based on the premise that using core ideas throughout mathematics curricula may facilitate the transition from earlier to more advanced courses, I analyse epistemologically to what extent the idea of averaging may be transferred to complex path integrals. In this case, the transition poses special epistemological challenges. Using an example from an expert interview, in which the expert aims to apply the interpretation of integrals as averages to complex path integrals, I illustrate the aforementioned challenges empirically.

AB - The transition from Riemann integrals to other real integrals has been discussed previously in mathematics education literature. In this transition, the interpretation of integrals as averages of the integrated functions generalises smoothly to measure and probability theory. In this paper, I address the transition to complex path integrals. Based on the premise that using core ideas throughout mathematics curricula may facilitate the transition from earlier to more advanced courses, I analyse epistemologically to what extent the idea of averaging may be transferred to complex path integrals. In this case, the transition poses special epistemological challenges. Using an example from an expert interview, in which the expert aims to apply the interpretation of integrals as averages to complex path integrals, I illustrate the aforementioned challenges empirically.

KW - Complex analysis

KW - integrals

KW - mean values

KW - epistemology of mathematical objects

KW - basic ideas

UR - http://www.scopus.com/inward/record.url?scp=85184449844&partnerID=8YFLogxK

U2 - 10.1080/0020739X.2024.2304882

DO - 10.1080/0020739X.2024.2304882

M3 - Article

JO - International Journal of Mathematical Education in Science and Technology

JF - International Journal of Mathematical Education in Science and Technology

SN - 0020-739X

ER -

Von denselben Autoren