Exploring mathematical connections in the context of proof and mathematical argumentation: A new proposal of networking of theories
Camilo Andrés Rodríguez-Nieto 1 * , Jonathan Alberto Cervantes-Barraza 2 , Vicenç Font Moll 3
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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

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