masterThesis
A ideia fundamental de variação no contexto da matemática do Ensino Médio
Fecha
2022-02-21Registro en:
DOMINGOS, João Victor de Menezes. A ideia fundamental de variação no contexto da matemática do Ensino Médio. 2022. 170f. Dissertação (Mestrado Profissional em Ensino de Ciências Naturais e Matemática) - Centro de Ciências Exatas e da Terra, Universidade Federal do Rio Grande do Norte, Natal, 2022.
Autor
Domingos, João Victor de Menezes
Resumen
Variation is one of the fundamental ideas of Mathematics suggested by Brazil’s High School
National Common Curricular Basis (BNCC, 2018), which guides the construction of school
curricula, in particular of the Algebra thematic unit. This piece of research aims at contributing
to the formation of high school students' variational thought through building assignments
focused on that fundamental idea of Mathematics. Therefore, part of our hipotheses is to
consider that one of the lacks in learning some school Mathematics concepts may be associated
to the initial contact that students have with the idea of variation during their journey through
basic education. That situation is being confirmed by pieces of research that develop proposals
for the teaching of Mathematics and, to those pieces, the fundamental idea of variation does not
seem to be in the basis of mathematical concepts teaching. Instead, that place is occupied by
traditional pedagogical approaches marked by the Modern Mathematics Movement and that
take the axioms of the Set Theory to Mathematics teaching activities in basic education. In that
sense, the activities that constitute the educational product, the guideline of this research, seek
to answer the following question: what contributions does the fundamental idea of variation
offer the formation of school Mathematics? For that purpose, proposals of tasks have been built,
applied and validated in the form of Teaching Orientation Activities (AOE), which, according
to Moura (2016), constitute the steps of organization of the pedagogical activity, as well as
serving as a potential instrument of learning analysis in teaching proposals and being our main
theoretical and methodological referential. We classify this piece of research as of qualitative
nature, given that, among other characteristics, it possesses an analytical-descriptive character
and its validation and data analysis happened in a natural context in an inductive process
(FONTES, 2019). As a result of the analytical-inductive discussion of the data production,
related to Caraça’s (1951) studies of the fundamental role that the idea of variation occupies in
the construction of mathematical knowledge, as well as Thomson and Carlson’s (2017) research
in what comes to students' levels of variational and covariational reasoning in school
Mathematics activities, we point out that working with the idea of variation and covariation has
made more profound discussions about important mathematical concepts possible, such as:
recognizing and defining discreet and continuous variables; the role of parameters and
equations coefficients in variables’ variational and covariational behavior in model analysis;
the importance of transitioning among different forms of representation in the analysis and
comprehension of variational and covariational relations (numeric/tabular, analytical or
graphical); as well as the role of the fundamental idea of variation in an integral human
formation. At this point, questions arise, such as: what other mathematical concepts may be
learned from the fundamental idea of variation? Because of that, we support the development
of other studies that may take the fundamental idea of variation, as an object of central
knowledge in the pedagogical activity, to the scenario of mathematical education.