A Didactic Engineering in the Research Process of the Generalization of the Padovan Sequence: An Experience in a Pre-Service Teacher Training Course

Abstract

Background: Obstacles are found during the epistemological construction of mathematical concepts research, aiming to contribute to the Didactics of Mathematics through a study of Padovan sequence. Objectives: describe elements of a systematic study, based on Didactic Engineering in conjunction with the Theory of Didactic Situations. I addition, referring to the generalization model of Padovan sequence and promoting a historical-evolutionary understanding and its mathematical properties. Design: it presents the most representative data of an investigation supported by the foundations of Didactic Engineering research design, in association with the Theory of Didactic Situations teaching methodology. Setting and Participants: the research was developed in 2019 and applied in a Pre-Service Mathematics Teacher Training Course in the History of Mathematics discipline, with the eight students enrolled. Data collection and analysis: data validation occurred internally due to the short period of the research. Results: it describes an investigation around the object of study, the Padovan sequence, focusing on the generalization process of this sequence and its properties. Thus, three problem situations are elaborated and analyzed based on the assumed research and teaching methodologies, seeking to examine their properties and the student's intuitive thinking, before the insertion of a historical-epistemological conception of this investigation. Conclusions: the research makes it possible to extract repercussions, suggest and promote research scripts aiming at the formation of teachers (initial) in the context of the teaching of History of Mathematics.