The Construction of Definitions Through Padovan’s Combinatorial Model: An Investigation With Didactic Engineering in an Initial Education Course for Mathematics Teachers

Abstract

Background: Given the oversight of specific topics in the history of mathematics books, this research was motivated by the extensive coverage of the Fibonacci sequence. In addition, the existence of the Padovan sequence, which is considered a Fibonacci cousin, stands out. Objectives: Investigating the Padovan sequence, building its definition through a combinatorial model using manipulative materials based on the theory of didactical situations in the initial mathematics teacher education course context. Design: The research methodological design follows didactic engineering, and a didactic teaching situation is created to investigate the Padovan sequence. Thus, manipulative material was developed to facilitate the teaching process and the construction of the sequence definition. Settings and participants: The interventions were done in the mathematics degree course of a higher education institution in Fortaleza. Five students enrolled in the component of History of Mathematics participated in the study. Data collection and analysis: Data were collected during classes, recorded through photos and audio recordings, based on didactic engineering and the theory of didactical situations. Results: The most relevant result of this study is constructing the definition of the Padovan sequence through the manipulative material. Conclusions: We concluded that the research allowed an investigation of the Padovan sequence, enabling the visualisation of its terms and their integration with other mathematical contents, contributing to teaching these numbers.