Exploring mathematical connections in the context of proof and mathematical argumentation: A new proposal of networking of theories
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1 Faculty of Natural and Exact Sciences, University of the Coast (CUC), Barranquilla, COLOMBIA2 Faculty of Education Sciences, Atlantic University, Barranquilla, COLOMBIA3 Department of Didactics of Experimental and Mathematical Sciences, University of Barcelona, Barcelona, SPAIN* Corresponding Author
Abstract
Extended theory of mathematical connections (ETC) and theory of mathematical argumentation (TMA) based on Toulmin’s (1984) model were articulated for the study of mathematical connections activated in the argumentation process. For this purpose, a “networking of theories” was made to obtain the complementarities between both theories. Then, a class episode was selected that dealt with the demonstration of the continuity theorem of functions of real variable “if a function is derivable at a point then it is continuous at that point”, made by an in-service mathematics teacher of differential calculus, who participated in a non-participant observation, where his classes were videotaped. The arguments of this episode were analyzed through with Toulmin’s (1984) model, after with thematic analysis method to identify mathematical connections, and, finally, the connections in the proof and mathematical argumentation were analyzed. The main result of the research reveals that the mathematical connections play a fundamental role in the argumentation process of the episode, given that, connection is important for the establishment and identification the argument and the warrant that supports it. In addition, complementarities were found between both theories, which makes this networking a useful tool for a better analysis of mathematical argumentation processes.
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Article Type: Research Article
EURASIA J Math Sci Tech Ed, 2023, Volume 19, Issue 5, Article No: em2264
https://doi.org/10.29333/ejmste/13157
Publication date: 01 May 2023
Online publication date: 03 Apr 2023
Article Views: 1213
Article Downloads: 749
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How to cite this article
APA
Rodríguez-Nieto, C. A., Cervantes-Barraza, J. A., & Font Moll, V. (2023). Exploring mathematical connections in the context of proof and mathematical argumentation: A new proposal of networking of theories. Eurasia Journal of Mathematics, Science and Technology Education, 19(5), em2264. https://doi.org/10.29333/ejmste/13157
Vancouver
Rodríguez-Nieto CA, Cervantes-Barraza JA, Font Moll V. Exploring mathematical connections in the context of proof and mathematical argumentation: A new proposal of networking of theories. EURASIA J Math Sci Tech Ed. 2023;19(5):em2264. https://doi.org/10.29333/ejmste/13157
AMA
Rodríguez-Nieto CA, Cervantes-Barraza JA, Font Moll V. Exploring mathematical connections in the context of proof and mathematical argumentation: A new proposal of networking of theories. EURASIA J Math Sci Tech Ed. 2023;19(5), em2264. https://doi.org/10.29333/ejmste/13157
Chicago
Rodríguez-Nieto, Camilo Andrés, Jonathan Alberto Cervantes-Barraza, and Vicenç Font Moll. "Exploring mathematical connections in the context of proof and mathematical argumentation: A new proposal of networking of theories". Eurasia Journal of Mathematics, Science and Technology Education 2023 19 no. 5 (2023): em2264. https://doi.org/10.29333/ejmste/13157
Harvard
Rodríguez-Nieto, C. A., Cervantes-Barraza, J. A., and Font Moll, V. (2023). Exploring mathematical connections in the context of proof and mathematical argumentation: A new proposal of networking of theories. Eurasia Journal of Mathematics, Science and Technology Education, 19(5), em2264. https://doi.org/10.29333/ejmste/13157
MLA
Rodríguez-Nieto, Camilo Andrés et al. "Exploring mathematical connections in the context of proof and mathematical argumentation: A new proposal of networking of theories". Eurasia Journal of Mathematics, Science and Technology Education, vol. 19, no. 5, 2023, em2264. https://doi.org/10.29333/ejmste/13157