Representaciones semióticas de objetos matemáticos y articulación de sentidos en situaciones de tratamiento. El caso de los profesores de matemáticas

Abstract

This research focuses on the cognitive transformation of treatment oriented: on the one hand, to document the phenomenon related to the difficulties encountered by some teachers to articulate the senses assigned to semiotic representations of the same mathematical object, obtained through treatment; and on the other, to establish similarities and differences of these difficulties with those that students encounter when solving mathematical tasks that require treatment reported in the literature. A collective case study is carried out with 11 mathematics teachers [5 primary and 6 secondary], selected as a result of the solutions made by 64 teachers [32 primary and 32 secondary], who do not carry out a minimum semiotic articulation in three Tasks, that is, those teachers who from the syntactic point of view admit the equivalence between expressions or representations, but from the semantic aspect these expressions or representations are associated with different mathematical objects or situations, thus preventing the relationship between the assigned meanings. these. The processes of assigning meanings of 11 mathematics teachers are described and analyzed in relation to four specific tasks, which investigates the meaning assigned to certain semiotic representations that requires the performance of treatment transformations, as well as their necessary articulation. A qualitative research approach of a descriptive-interpretive type is assumed, from two theoretical perspectives: the theory of semiotic transformations proposed by Raymond Duval (1993, 2017) that allowed to describe, consolidate and locate the research problem in the field of research of the transformations; and the theory of the ontosemiotic approach proposed by, Juan D. Godino and his collaborators (1994, 2019) in as much, provides tools to analyze and explain the solutions given by teachers that highlight the personal meanings given to semiotic representations obtained by treatment. The present study provided elements that made it possible to identify the difficulties that mathematics teachers encounter in articulating the senses assigned to semiotic representations obtained through treatment: the difficulties that mathematics teachers encounter were contrasted with the difficulties encountered by students, aspects that allow us to conclude that both teachers and students adequately perform the required treatments that allow them to admit the equivalence between expressions from the syntactic plane, but giving meaning and meaning to the expressions related in the tasks prevents them from making the same recognition