Abstract

PECHARROMAN, Cristina; ARCE, Matías; CONEJO, Laura  and  ORTEGA, Tomás. Theoretical methodology to analyze the degree of congruence between representations of mathematical objects: the case of the unbounded intervals of the real line. Educ. mat. [online]. 2018, vol.30, n.3, pp.184-210.  Epub Feb 07, 2022. ISSN 2448-8089.  https://doi.org/10.24844/em3003.08.

According to Duval (1999, 2006), it is considered that the apprehension of a concept involves the comprehensive and natural use of its representations, and that the ability to make conversions between representations is critical for it. This issue is particularly important in mathematical objects with a complex conceptualization, such as the intervals of the real line in secondary education. This article presents a theoretical methodology to analyze the degree of congruence between several representations of a mathematical object. In this methodology, we adapt and expand the three criteria given by Duval (1999), creating a congruence rate of a conversion between representations of a mathematical object. The application of the methodology of analysis is illustrated through the case of the unbounded intervals of the real line. Assuming that less congruence between representations produces learning difficulties inherent in the object, we use the results obtained to propose some reflections and recommendations on the learning of unbounded intervals of the real line.

Keywords : interval; real line; representations; congruence, difficulty of a conversion.