Systemic-functional analysis of algebraic texts: towards an understanding of their discursive nature in history and some implications in their teaching - López-Acosta, Luis Alberto; Rodríguez-Vergara, Daniel (IE Revista de Investigación Educativa de la REDIECH, 2021)
In mathematics education the study of algebraic language has focused mainly on the semantic and syntactic aspects of its symbolism, so little has been studied about the relationship between the component of natural and symbolic languages. Therefore, in this paper we report a systemic-functional and multisemiotic analysis of the experiential component in ancient algebraic texts relevant to the history of algebra. The relevance of these texts was determined through a previous historical epistemological study that sought to recover less known concepts in their current didactics that could pose elements to be considered in the teaching and learning of algebraic language. Based on some epistemological considerations, the system of transitivity of the Systemic-Functional Linguistic Theory was adapted for these purposes, obtaining that symbolism is not an autonomous semiotic resource in these texts, besides that the participants and processes within these refer to mathematical objects that are not catalogued only as numerical. These results contrast with the typical characterization of algebra as a language of symbols.