Details
| Original language | English |
|---|---|
| Journal | International Journal of Mathematical Education in Science and Technology |
| Publication status | E-pub ahead of print - 7 Feb 2024 |
Abstract
Keywords
- Complex analysis, integrals, mean values, epistemology of mathematical objects, basic ideas
ASJC Scopus subject areas
- Social Sciences(all)
- Education
- Mathematics(all)
- Applied Mathematics
- Mathematics(all)
- Mathematics (miscellaneous)
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In: International Journal of Mathematical Education in Science and Technology, 07.02.2024.
Research output: Contribution to journal › Article › Research › peer review
}
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 -