Banca de QUALIFICAÇÃO: RANNYELLY RODRIGUES DE OLIVEIRA

Uma banca de QUALIFICAÇÃO de DOUTORADO foi cadastrada pelo programa.
STUDENT : RANNYELLY RODRIGUES DE OLIVEIRA
DATE: 30/11/2022
TIME: 14:00
LOCAL: remota
TITLE:

THE STUDY OF HAMILTON'S QUATERNIONS ENLIGHTENING QUESTIONS ABOUT THE NATURE OF MATHEMATICS

KEY WORDS:

Mathematics Education. History of Mathematics. Hamiltonian quaternions. Nature of Mathematics. Teaching Training

PAGES: 91
BIG AREA: Ciências Humanas
AREA: Educação
SUBÁREA: Tópicos Específicos de Educação
SUMMARY:

This research is being developed within the scope of Mathematics Education (EM), in which we address the insertion of the History of Mathematics (HM) in Teacher Training (FD). In this vein, Brito (2007) argues that HH can contribute to DF, filling the gap between specific training, pedagogical training and teaching practice. Morey (2013) proposes the use of the historical (original) source as a strategy for inserting HH in MI. In this way, we intend, from an exemplary case study, to show possibilities and contributions of HH in FD. In view of this, we assume the following research questions: What contributions can the history of quaternions provide to the training of Mathematics teachers? What philosophical, conceptual and contextual aspects of Mathematics does this case study reveal? The general objective of this research is to investigate the history of quaternions from the philosophical, conceptual and contextual perspectives to clarify how to build a narrative that brings contributions to the training of Mathematics teachers. For this, a search and bibliographical analysis of primary and secondary sources related to the quaternions theme during the 19th century was carried out and a historical narrative was made, highlighting elements that can contribute to the training of Mathematics teachers. The historical study of this research is mainly based on the works of Hamilton (1866), Robert Graves (1882, 1885, 1889) and Hankins (1980). The historical narrative we developed highlights the contextual, philosophical and conceptual aspects that were revealed when we came to understand quaternions as a product of human action and as part of an unfinished Mathematics, whose development is non-linear, non-continuous and non-progressive. From a historiographical perspective, we consider the contextual and temporal contingencies pertinent to the historical development of the quaternions. We consider Fried's (2001) ideas pertinent to the dual synchronic and diachronic view that evidences Mathematics, according to Fried (2008), as a set of signs and a product of human action. In this sense, we seek to know which nature of the quaternions could be revealed in this historical study. Thus, the justification that fostered this research is based on the double vision (synchronic and diachronic) that reveals the nature of quaternions and their possible implications in the training of Mathematics teachers. Therefore, we can understand, that for the understanding of the quaternions in its totality, it is necessary to study it synchronic and diachronically. With this, we understand that quaternions are composed of human actions and sign systems. The human aspects are explicit when Hamilton proposed algebra as a science of pure time assuming assumptions of an intuitive order. The formalization of quaternions as a system of signs occurs through their algebraic constitution (imaginary components and operations). Finally, we intend to carry out a pedagogical intervention that allows the understanding of the contextual, philosophical and conceptual aspects of the historical development of the quaternions through the discussion of this historical narrative in the FD, in order to provide the licensee with the opportunity to develop a conception about the nature of Mathematics that part of the Friedian double vision.

COMMITTEE MEMBERS:
Interna - ***.667.318-** - ANA PAULA BISPO DA SILVA - UEPB
Interna - 1169920 - BERNADETE BARBOSA MOREY
Externa à Instituição - CIBELLE CELESTINO SILVA - USP