A didactic engineering for the study of the Padovan’s combinatory model
Renata Passos Machado Vieira 1 * , Francisco Regis Vieira Alves 2 , Paula Maria Machado Cruz Catarino 3
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1 Polo RENOEN-Universidade Federal do Ceará, Fortaleza, BRAZIL2 Federal Institute of Science and Technology Education of the State of Ceara, Fortaleza, BRAZIL3 University of Trás-os-Montes and Alto Douro, Vila Real, PORTUGAL* Corresponding Author


Considering the content of history of mathematics textbooks, it’s evident that their emphasis is primarily on the illustrative aspects of recurring numerical sequences, with a particular focus on the Fibonacci sequence. Unfortunately, this limited approach results in the neglect of other sequences akin to the Fibonacci numbers, thus rendering the subject challenging for teaching purposes. This study aims to address this gap by offering a concise exploration of the combinatorial aspects of the Padovan numbers, specifically through the concept of a board as initially examined by mathematicians. In line with the research methodology of didactic engineering and the teaching theory of the theory of didactic situations, two problem situations have been developed, centered on the Padovan combinatorial model, thereby contributing to the enrichment of mathematical education within initial teacher training programs. Within this framework, various strategies are introduced that rely on visualization and counting, with the objective of illustrating specific mathematical identities suitable for potential classroom applications.


This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

PEDAGOGICAL RES, Volume 9, Issue 3, July 2024, Article No: em0206


Publication date: 01 Jul 2024

Online publication date: 04 Apr 2024

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