Níveis de desenvolvimento do pensamento algébrico : um modelo para os problemas de partilha de quantidade

Abstract

This thesis aimed to propose a model that allows the identification of levels of development of algebraic thinking revealed by students to solve partition problems. Our research was conducted in two stages. The first built a previous version of the model after analysis of Oliveira and Câmara (2011) and Santos Junior (2013) results, and the responses of 342 students from the 6th grade of elementary school, 195 Brazilian students from three schools of the metropolitan region of Recife and 147 Canadian students from four schools in the province of Quebec to a questionnaire composed of six partition problems. In the second stage we seek to validate our model. For this, we reapplied the questionnaire used in the first stage to 343 students of the final years of elementary education at two schools in the city of Recife, 72 of the 6th year, 83 of the 7th year, 93 of the 8th year and 95 the 9th year and conducted a explicitness interview with eight students, two from each level of the model. At the end we arrive at the proposition of an algebraic thinking model that goes from level 0, characterized by the absence of algebraic thinking, through an incipient level of algebraic thinking (level 1) for an intermediate level (level 2) and a consolidated level of algebraic thinking (level 3). We also propose to each level, from level 1, three sublevels, which we call sublevels A, B and C.