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RESEARCH PAPER
Exploring mathematical connections in the context of proof and mathematical argumentation: A new proposal of networking of theories
1
Faculty of Natural and Exact Sciences, University of the Coast (CUC), Barranquilla, COLOMBIA
2
Faculty of Education Sciences, Atlantic University, Barranquilla, COLOMBIA
3
Department of Didactics of Experimental and Mathematical Sciences, University of Barcelona, Barcelona, SPAIN
Online publication date: 2023-04-03
Publication date: 2023-05-01
EURASIA J. Math., Sci Tech. Ed 2023;19(5):em2264
KEYWORDS
networking of theoriesextended theory of connectionstheory of mathematicalargumentationproofderivative
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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