Banca de DEFESA: JÉSSICA CRAVO SANTOS BERNARDINO

AUXILIARY REPRESENTATIONS AND DESIGNATION OPERATIONS: Contributions to the development of algebraic thinking from the resolution of quantity sharing problems

Auxiliary Representations; Semiotic Representation Register Theory; cognitive operations of designation; Quantity-Sharing Problems; Algebraic Thinking.

The present text presents partial results of a doctoral research that aims to analyze the contributions of the operations of assignment, auxiliary representations and the functions assigned to them, in the development of algebraic thinking of students from 6th to 9th grade of elementary school, from the resolution of problems of quantity sharing. Having the Theory of Semiotic Representation Registers as theoretical support, recommended by Raymond Duval (2004a, 2004b, 2007, 2011, 2012, 2016), the proposal has as central question to answer the following inquiry: what are the operations of designation, the types of auxiliary representation, their function and how they contribute to the development of the student's algebraic thinking in solving problems of sharing quantity? So far, a preliminary analysis of the data was performed, considering the protocols of Oliveira and Câmara dos Santos (2011), to categorize the types of auxiliary representations identified in solving sharing problems by 6th grade students, seeking to verify, also, what is the functionality attributed to these auxiliary representations. From the analysis performed it was possible to identify 7 types of auxiliary representations used in problem solving, such as: illustrative drawing, mixed, space to be filled, drawing by units, table, columns and scheme, and four functions identified by these representations, with the role of organization, illustration, selection of relevant or material elements. An analysis in terms of the cognitive operations of designation will prove or disprove this classification, varying the factors of semantic noncongruence, whose purpose is to understand how the operations of designation and auxiliary representations contribute to the development of student's algebraic thinking, as characterized by Almeida (2016), Radford (2010), Brandt et al (2018) and Duval (2002, 2004b, 2011, 2020).