Desenvolvimento do pensamento algébrico nos cadernos de matemática do ciclo de alfabetização do Programa Soma

Abstract

Considering the relevance of teaching algebra from the early years of schooling, for the development of students' algebraic thinking, understandings of future studies in algebra and apprehensions of mathematical knowledge. It is also an emerging theme, in curriculum elaboration, practic and academic educational research. The present doctoral research analytically studied the Mathematics Notebooks for teachers, from the Collection of Literacy Practices in the literacy Cycle, of the SOMA Program. The general objective, is to start from the understanding that the development of algebraic thinking takes place in a relational perspective, to analyze how the didactic tasks/suggestions proposed in the Math Notebooks for the SOMA literacy Cycle, can contribute to the teacher's work in promoting the development of algebraic thinking. Our specific objectives are: show whether and how the didactic tasks/suggestions cover the knowledge and skills foreseen for each of the years of education covered by SOMA, considering the current version of the Common National Curricular Base; indicate, when necessary, approachs/strategies that enable the teacher to extend the potential of the tasks to promote the development of algebraic thinking. In the theoretical and epistemological organization of this study, our foundation is based on the conception of Fonseca (2014), when it comes to mathematical literacy. Regarding the development of algebraic thinking, we draw on the studies of Kieran (2004, 2007, 2011), Kieran, Pang, Schifter and Ng (2016), Blanton and Kaput (2005), Carraher, Schliemann, Brizuela and Earnest (2006), Cai and Knuth (2011), Mason (2008), and, specifically, for the study of patterns, in Vale, Palhares, Cabrita and Borralho (2006), Vale and Pimentel (2011, 2013), Pimentel and Vale (2011). In the relational thinking approach we draw on Carpenter, Levi, Franke and Zeringue (2005), Jacobs, Franke, Carpenter, Levi and Battey (2007), Franke, Carpenter and Battey (2008), Empson, Linda and Carpenter (2011). This is a documentarytype investigation, as we surveyed and analyzed data in the Math Notebooks for the literacy Cycle of the SOMA Program. For the analytical treatment of the data collected, we established as method of analysis inferences, that is, interpreting and reflecting on the didactic tasks/suggestions. In the reflective analyses we verified that the didactic tasks/suggestions of the Math Notebooks for the SOMA literacy Cycle cover the realization of classifications, by means of numerical and geometrical atributes, and, especially, the 2nd and 3rd Year Notebooks, which encompass the establishment of relations, the discovery/elaboration of patterns, the identification of the next/absent elements, and the development of generalizations, in numerical and figurative sequences. These aspects are integral to the way of thinking algebraically.