Exploring the Relationship between Tacit Models and Mathematical Infinity through History

Autor/inn/en	Díaz-Chang, Tamara; Arredondo, Elizabeth-H.
Titel	Exploring the Relationship between Tacit Models and Mathematical Infinity through History
Quelle	In: International Electronic Journal of Mathematics Education, 18 (2023) 2, (11 Seiten)Infoseite zur Zeitschrift PDF als Volltext kostenfreie Datei Verfügbarkeit
Zusatzinformation	ORCID (Díaz-Chang, Tamara) ORCID (Arredondo, Elizabeth-H.)
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
Schlagwörter	Epistemology; Mathematical Concepts; Mathematical Models; Ethnography; Abstract Reasoning; Comprehension; History + Suchen Sie Ihr Suchwort? Erkenntnistheorie; Mathematical model; Mathematisches Modell; Ethnografie; Abstraktes Denken; Denken; Verstehen; Verständnis; Geschichte; Geschichtsdarstellung
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. (As Provided).
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Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2024/1/01