Undergraduates’ exploration of contour integration: What is Accumulated?

Soto, Hortensia; Oehrtman, Michael

doi:10.1016/j.jmathb.2022.100963

Cited by 6 publications

(1 citation statement)

References 21 publications

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“…Studies in Mathematics Education have been carried out to address this type of problems. For example, some research has incorporated digital technologies to attend to different mathematical objects inscribed in the theory of complex functions (D'Azevedo & Dos Santos, 2021;Dittman et al, 2016;Ponce, 2019), while some other studies investigate how undergraduate mathematics students and professional mathematicians work geometrically with them (Hanke, 2020;Oehrtman et al, 2019;Soto & Oehrtman, 2022;Soto-Johnson et al, 2016).…”

Section: Introductionmentioning

confidence: 99%

What enabled the production of mathematical knowledge in complex analysis?

Piña-Aguirre

Farfán

2023

INT ELECT J MATH ED

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With the objective of identifying intrinsic forms of mathematical production in complex analysis (CA), this study presents an analysis of the mathematical activity of five original works that contributed to the development of Cauchy’s integral theorem. The analysis of the mathematical activity was carried out through the identification of the types of expressions used and the way they were used by the historical subjects when communicating their results, to subsequently identify transversal elements of knowledge production. The analysis was refined by the notion of confrontation, which depicts the development of mathematical knowledge through the idea of building knowledge against previous knowledge. As a result of the study we established epistemological hypothesis, which are conceived as conjectures that reveal ways in which mathematical knowledge was generated in CA.

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Section: Introductionmentioning

confidence: 99%

What enabled the production of mathematical knowledge in complex analysis?

Piña-Aguirre

Farfán

2023

INT ELECT J MATH ED

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Actualizing the virtuality of the Cauchy-Riemann equations

Soto,

Abbrescia,

Castillo

et al. 2024

ZDM Mathematics Education

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Experts’ intuitive mathematical discourses about integration in complex analysis

Hanke

2024

ZDM Mathematics Education

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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.

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Undergraduates’ exploration of contour integration: What is Accumulated?

Cited by 6 publications

References 21 publications

What enabled the production of mathematical knowledge in complex analysis?

What enabled the production of mathematical knowledge in complex analysis?

Actualizing the virtuality of the Cauchy-Riemann equations

Experts’ intuitive mathematical discourses about integration in complex analysis

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