Teoria dos registros de representação semiótica: as atividades cognitivas de tratamento e conversão mobilizadas em aulas de matemática sobre porcentagem.

Abstract

For mathematical learning, it is considered that fundamental cognitive activities such as conceptualization, reasoning, problem solving and text comprehension require the use of systems of expression and representation. For mathematical comprehension, it is possible to adhere to the use of semiotic representations through a variety of transformations between semiotic representation registers (srr). Based on the idea that these transformations can be more or less immediate and their relevance to learning mathematics, the aim of this research was to show how transformations of treatment and conversions between different srr were requested and mobilized in mathematics classes. The aim was to answer the following question: in what way was coordination between the different semiotic representation registers requested during the mathematics lessons on percentages offered on the Aula Paraná channel, and how were the treatments and conversions between them mobilized? To this end, we analyzed four lessons, each lasting approximately 45 minutes, which totaled 25 tasks on percentages. These were offered to 6th grade students on the Aula Paraná channel on the YouTube platform, during the context of the Covid-19 pandemic in 2020. Raymond Duval's Theory of Semiotic Representation Registers (TSRR) was used as a theoretical framework. The analysis included transcribing the teachers' speeches, describing the moments when the content was explained, the proposed activities and their respective resolutions. In addition, a table was drawn up to guide the identification of the starting and ending registers and semantic congruence criteria. The analysis revealed conversion activities between srr figural to srr natural language, srr figural to srr numeric, srr natural language to srr numeric, srr numeric to srr numeric, srr numeric to srr natural language and srr numeric to srr figural. The most common conversion activity was between numeric srr and numeric srr. It is hoped that this text will contribute to reflections on the importance of the activity of conversion, a cognitive activity characterized by the transformation of a register belonging to one semiotic system of representation into another register belonging to another semiotic system of representation. This is characterized by the presence of the semantic congruence criteria: semantic correspondence; semantic univocity and organization of the units of meaning. In this way, it was elucidated how the conversion occurred, based on these criteria, in tasks developed in the mathematics classes analyzed, about percentages.