Modelo epistemológico meta-analítico relativo à noção de raciocínio combinatório

Abstract

This research aims to develop an epistemological study on notions of combinatorial reasoning in theses and dissertations defended between 1998 and 2019, resulting from masters and doctoral research, in Brazil, based on Qualitative Meta-Analysis, which will be used to build and analyze theses and dissertations, based on an Analytical Model for the Notion of Combinatorial Reasoning. Qualitative Meta-Analysis, associated with the Anthropological Theory of Didactics (TAD), is taken as a theoretical and methodological reference, based on the guidelines of the National Common Curricular Base and Fischbein's proposals. The thesis is organized into two major moments: studies of the teaching problem and the epistemological dimension and studies of the economic-institutional and ecological dimensions. The result obtained from the research demonstrates that the Analytical Model and the Notion of Combinatorial Reasoning play an important role in understanding the problems associated with counting, in three Levels: Level I - Absence of Multiplicative Systematization: at this level, subjects contextualize their answers, though without hints of combinatorial reasoning in his effort to find the solution to the problem; Level II – Beginning of Multiplicative Systematization: at this level, subjects are able to properly order and rank the variables, but cannot dissociate them, making them vary at the same time, which makes it impossible to verify the correct solution; and Level III – Generalizing Systematizations: at this level, the main property of formal thinking is the insertion of reality as a subset of a larger set of possibilities. Instead of theorizing about (concrete) empirical data, formal thinking allows the subject to theorize about possibilities. The bibliographical study linked to the Analytical Model applied to two collections of textbooks allowed a minimum structuring of criteria to analyze didactic materials, more specifically, textbooks, with the praxeological approach of TAD, making it possible to insert this analysis in one of the categories of the Analytical Model.