Exploring the relationship between tacit models and mathematical infinity through history

Tamara Díaz-Chang; Elizabeth-H Arredondo

doi:10.29333/iejme/12823

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Tamara Díaz-Chang ¹ ² ^* , Elizabeth-H Arredondo ²

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¹ Instituto de Ciencias Físicas y Matemáticas, Universidad Austral de Chile, Valdivia, CHILE² Department of Exact Sciences, Universidad de Los Lagos, Osorno, CHILE^* Corresponding Author

Abstract

In this article we address the historical and epistemological study of infinity as a mathematical concept, focusing on identifying difficulties, counter-intuitive ideas and paradoxes that constituted implicit, unconscious models faced by mathematicians at different times in history, representing obstacles in the rigorous formalization process of this mathematical concept. It is shown how the active and conscious questioning of these models led to a process of axiomatization of mathematical infinity, which was completed with the works of Cantor (1883) and Robinson (1974). The implemented methodology is supported by a qualitative and argumentative bibliographic research based on content analysis from a meta-ethnography. From this research, information is obtained about the unconscious mathematical structures students are confronted with and the conscious patterns of reasoning they must develop to overcome difficulties and obstacles that these models produce, and thus achieve an adequate understanding of mathematical infinity.

Keywords

implicit knowledge
unconscious learning
historical-epistemological study

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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

INT ELECT J MATH ED, 2023, Volume 18, Issue 2, Article No: em0730

https://doi.org/10.29333/iejme/12823

Publication date: 01 Apr 2023

Online publication date: 09 Jan 2023

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How to cite this article

APA

Díaz-Chang, T., & Arredondo, E.-H. (2023). Exploring the relationship between tacit models and mathematical infinity through history. International Electronic Journal of Mathematics Education, 18(2), em0730. https://doi.org/10.29333/iejme/12823

Vancouver

Díaz-Chang T, Arredondo EH. Exploring the relationship between tacit models and mathematical infinity through history. INT ELECT J MATH ED. 2023;18(2):em0730. https://doi.org/10.29333/iejme/12823

AMA

Díaz-Chang T, Arredondo EH. Exploring the relationship between tacit models and mathematical infinity through history. INT ELECT J MATH ED. 2023;18(2), em0730. https://doi.org/10.29333/iejme/12823

Chicago

Díaz-Chang, Tamara, and Elizabeth-H Arredondo. "Exploring the relationship between tacit models and mathematical infinity through history". International Electronic Journal of Mathematics Education 2023 18 no. 2 (2023): em0730. https://doi.org/10.29333/iejme/12823

Harvard

Díaz-Chang, T., and Arredondo, E.-H. (2023). Exploring the relationship between tacit models and mathematical infinity through history. International Electronic Journal of Mathematics Education, 18(2), em0730. https://doi.org/10.29333/iejme/12823

MLA

Díaz-Chang, Tamara et al. "Exploring the relationship between tacit models and mathematical infinity through history". International Electronic Journal of Mathematics Education, vol. 18, no. 2, 2023, em0730. https://doi.org/10.29333/iejme/12823