Hibridização dos números triangulares: uma análise preliminar e a priori e a visualização por meio do software GeoGebra

Francisco Evamar Barros; Francisco Regis Vieira Alves; Milena Carolina dos Santos Mangueira; Renata Passos Machado Vieira; Paula Maria Machado Cruz Catarino

doi:10.34624/id.v12i3.20106

Authors

Francisco Evamar Barros Instituto Federal de Educação, Ciência e Tecnologia do Estado do Ceará – IFCE https://orcid.org/0000-0002-8568-7854 (unauthenticated)
Francisco Regis Vieira Alves Instituto Federal de Educação, Ciência e Tecnologia do Estado do Ceará – IFCE https://orcid.org/0000-0003-3710-1561 (unauthenticated)
Milena Carolina dos Santos Mangueira Instituto Federal de Educação, Ciência e Tecnologia do Estado do Ceará – IFCE https://orcid.org/0000-0002-4446-155X (unauthenticated)
Renata Passos Machado Vieira Instituto Federal de Educação, Ciência e Tecnologia do Estado do Ceará – IFCE https://orcid.org/0000-0002-1966-7097 (unauthenticated)
Paula Maria Machado Cruz Catarino CIDTFF, Universidade de Trás-os-Montes e Alto Douro – UTAD https://orcid.org/0000-0001-6917-5093 (unauthenticated)

DOI:

https://doi.org/10.34624/id.v12i3.20106

Keywords:

Didactic Engineering, Teaching, Triangular hybrid numbers, software, of Didactic Situations

Abstract

This paper discusses the first two phases of Didactic Engineering, supported by the teaching theory, Theory of Didactic Situations, with the aim of developing a study about the hybridization process of triangular numbers, through teaching didactic situations based on the first two Didactic Engineering phases. Considered absent in many contents explored in the area of teaching and in the History of Mathematics, the object of study, referring to triangular hybrid numbers, is presented in this research, in order to discuss some mathematical properties, in addition to highlighting some epistemological, cognitive elements and didactic. Undoubtedly, two problem situations are explored, related to the way of visualizing these numbers through software and, regarding their generating function, supported by the phases of teaching theory, highlighting possible behaviors of students in initial teacher training courses. It is worth noting that certain elements are analyzed, in view of a possible posterior analysis of Didactic Engineering.