Banca de QUALIFICAÇÃO: RANNYELLY RODRIGUES DE OLIVEIRA

Uma banca de QUALIFICAÇÃO de DOUTORADO foi cadastrada pelo programa.
STUDENT : RANNYELLY RODRIGUES DE OLIVEIRA
DATE: 31/05/2022
TIME: 14:00
LOCAL: remota
TITLE:

THE CONCEPTUAL AND ALGEBRAIC DEVELOPMENT OF QUATERNIONS FROM THE HEURISTIC PATH OF WILLIAM ROWAN HAMILTON

KEY WORDS:

History of Mathematics. Quaternions. William Hamilton

PAGES: 100
BIG AREA: Ciências Humanas
AREA: Educação
SUBÁREA: Tópicos Específicos de Educação
SUMMARY:

This work has, in its scope, the historical investigation of quaternions, aiming at the rescue of their historical-mathematical value overshadowed by the traditional conceptions of Classical Algebra. The justification of this research lies in the recognition that, during the development of the Quaternions, there were contextual changes that influenced the construction of historiographical and epistemological conceptions that allowed us to look at Mathematics as non-linear, non-continuous and non-progressive. What could not be observed if this research was developed by the traditional historiographical strand. The object of investigation of this research is the historicity of the Quaternions. The objective is to carry out a historiographical, contextual and epistemological study of the Quaternions, with a view to recognizing their pedagogical potential in a space for teacher training. For this, the following guiding question was assumed: what historical and heuristic aspects influenced the development of the Hamiltonian quaternions and what pedagogical potentiality can be extracted from the historicity of the quaternions? Therefore, the History of Updated Mathematics was adopted as a theoretical-methodological contribution to the development of this thesis. A biographical research of William Rowan Hamilton and a theoretical survey about the Quaternions were carried out in the compendia of the History of Mathematics and in the didactic-cognitive context. And a study of primary and secondary sources that deal with the constitution and algebraic extension of Quaternions was carried out. It is worth mentioning that it was from the primary source that we tried to reach the historiographical, epistemological and contextual dimensions. It can be understood that contextual and temporal contingencies influence the formation of a researcher's heuristic profile and the meaning that the scientific body assumes. In this sense, it can be seen that the development of quaternions was characterized as a transition towards the emergence of non-commutative algebras. This algebraic extension does not translate a refutation of the validity of algebraic principles, but allows revealing the character of unfinished knowledge that Mathematics has. Furthermore, it is believed that the pedagogical approach of the Quaternions, through their historicity, can provide opportunities for knowledge about their algebraic constitution; considering the historiographical, contextual and epistemological aspects of its historical development; and recognition of the place that Quaternions occupy on the map of scientific knowledge. Finally, we intend to expand the historical narrative about the quaternions from the deepening of the analysis of their historiographical, epistemological and contextual dimensions.

BANKING MEMBERS:
Presidente - 095.667.318-09 - ANA PAULA BISPO DA SILVA - UEPB
Interna - 1169920 - BERNADETE BARBOSA MOREY
Externa à Instituição - CIBELLE CELESTINO SILVA - USP