A modelagem matemática em diálogos com a teoria da aprendizagem significativa e da teoria dos campos conceituais

Abstract

In preliminary studies on the theories of learning, we realized that Mathematical Modeling, Signia Learning Theory and Conceptual Fields Theory have, among themselves, at least one element in common, because the three themes carry as a premise the context of the classroom. The main objective of this thesis is to approximate theoretical and methodological foundations of Modeling to teach Mathematics with the theories of Meaningful Learning and Conceptual Fields. It is oriented from the following research question: what characteristics of Modeling to teach Mathematics can be epistemologically based on the theories of Meaningful Learning and Conceptual Fields? In this research, we turn our gaze to the researchers of Modeling to teach Mathematics most cited in the last National Conference on Modeling in Mathematics Education (CNMEM), held in 2019, with the objective of comcomworking the corpus of the research. We chose as methodology, to do the treatment of the data, the discursive textual analysis. The characteristics of Mathematical Modeling were constructed from the articles and books analyzed by researchers Almeida, Silva and Vertuan (2012), Barbosa (2001, 2003), Bassanezi (2019), Biembengut (2016) and Burak (2019), looking through the lens of Meaningful Learning and Conceptual Fields. It was possible to identify at least four characteristics of Modeling to teach Mathematics: the knowledge necessary for the modeling process, problem situations in the modeling process, the involvement of the modelers in the modeling process, the relationship between theory and practice in the modeling process and which are based on the theories of Meaningful Learning and Conceptual Fields, with regard to the following concepts: subsunçor, previous organizers, condition of significant learning, situations, adaptation, principle of the Theory of Conceptual Fields, schemes and operative invariants. Research has shown that subsumers are as important for Significant Learning Theory as for Modeling; if the learner or modeler does not have subsunçores, the processes do not happen. It was also identified that the subsunçores permeate the four characteristics of modeling to teach mathematics. The Modeling proved to be a potentially significant material: the students are motivated to want to learn, the situations indicated by Vergnaud converge with the situations worked in the modeling, because without situation there is no modeling. It was also identified that the scheme and operative invariants are of paramount importance for the Theory of Conceptual Fields as well as for modeling.