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.
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