Articulación y cambios de sentido en situaciones de tratamiento de representaciones simbólicas de objetos matemáticos

Abstract

In the process of teaching and learning of mathematics the use of representations of objects in a variety of semiotic representation systems, more specifically in diversity of semiotic records (Duval, 1999), but especially it becomes necessary to appropriate possibilities to transform a semiotic representation of one mathematical object in another. Such transformations between semiotic representations they occur both within the same semiotic representation register as between differentiated records, transformations that Duval calls treatments and conversions, respectively. Duval recognizes conversion as one of the fundamental cognitive operations for the subject's access to a true understanding, and focuses on the difficulties of mathematics learning in this process. However, in mathematics, the treatment transformations between semiotic representations - within the variety of records used - not only are they fundamental, but they could be source of difficulties in the processes of understanding mathematics by students. It is usually stated that cognitive problems are related to conversion, while what is related to treatment is not usually considered as a relevant problem for the construction of the mathematical object. That is, this author stands out explicitly the complexity involved in recognizing the same object through of completely different representations, as produced in semiotic systems heterogeneous (Conversion), but does not highlight the complexity associated with transformations made within the same semiotic system of representation (treatment). The present investigation is oriented to document the phenomenon related to the difficulties encountered by some students to articulate the senses assigned to semiotic representations of the same mathematical object, obtained by treatment. A description and analysis of the allocation processes of senses of nine students, six of 9th grade and three of 11th grade, based on work performed by them in three small groups in relation to specific tasks, in which inquire about the meaning assigned to certain semiotic representations and it is required to perform treatment transformations A qualitative research approach is assumed, performing a descriptive-interpretative analysis, from different perspectives theoretical, taking as reference works by Bruno D’Amore, Raymond Duval, Juan D. Godino and Luis Radford. Thus, this work is situated in a semiotic context, and studies in a general way the relationship semiosis-noesis in the construction of mathematical knowledge by students of 9th and 11th grades of basic and secondary education, respectively; study that without being exhaustive, includes aspects about mathematical activity, communication about objects emerging mathematicians and the cognitive construction of mathematical objects.