Achados sobre generalização de padrões ao “garimpar” pesquisas brasileiras de educação matemática (2003-2013)

Abstract

In this desk research study of the state-of-the-art type, the contribution of authors of Brazilian theses and dissertations on mathematics education published between 2003 and 2013 on the subject ‘generalization of mathematic patterns’ was assessed. The importance of the subject was characterized based on the ideas of Mason, Ferrini-Mundy, Lappan, Phillips, and Devlin about generalization of patterns and on some of the ideas of Dreyfus on processes of advanced mathematical thinking. In order to establish indicators for the inferences based on the documents investigated, Bardin’s content analysis approach was adopted. Searches were performed on the Capes database and on websites of 23 Brazilian institutions providing graduate programs stricto sensu in the teaching area. One thesis and 26 dissertations were selected and grouped into two categories: studies in which pattern generalization was a secondary topic and those in which it was the primary topic. It was concluded that the studies in both categories contributed on two main fronts: (1) the capacity that pattern generalization activities have to spark the curiosity of subjects, promoting the development of algebraic thinking, particularly with regard to generalization itself, a characteristic of the processes of advanced mathematical thinking (visualization, validation, investigation, representation, induction, synthesis, and abstraction, among others), and providing means for the subject to construct mathematical concepts (such as that of function); (2) the importance of pattern generalization activities being featured in all stages of basic education, including early grades, given that they provide teachers and students with a variety of algebra conceptions (particularly algebra as a way of thinking), inter-relating the various different aspects of algebraic thinking