As concepções sobre o Teorema fundamental da Aritmética de professores de Matemática da rede pública paulista, sob o olhar da teoria APOS

• Autor(a) principal: D’Almeida, Joice
• Data de Publicação: 2021
• Tipo de documento: Tese
• Idioma: por
• Título da fonte: Biblioteca Digital de Teses e Dissertações da PUC_SP
• Texto Completo: https://repositorio.pucsp.br/jspui/handle/handle/24520
• topic: CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA; Aritmética - Fundamentos; Teoria dos números; Matemática - Estudo e ensino; Arithmetic - Foundations; Number theory; Mathematics - Study and teaching

The central theme of this thesis is the Fundamental Theorem of Arithmetic, an integral part of the Elementary Theory of Numbers, whose main objective is to investigate the conceptions and knowledge of Mathematics teachers, working in the public schools in São Paulo, about the Fundamental Theorem of Arithmetic. The work, developed in the context of a qualitative research, had the participation of six volunteer Mathematics teachers working in the São Paulo public network. The theoretical foundation of the research was based on Ed Dubinsky's APOS theory, which describes the path to the construction of mathematical concepts, through mental mechanisms - interiorization, encapsulation and thematization - and mental structures, also called conceptions - Action , Process, Object and Schema. A Genetic Decomposition was elaborated, a component element of the theory used, in which the possible mental constructions that an individual builds for the understanding of the Fundamental Theorem of Arithmetic and the concepts linked to it were described. As an auxiliary theory in the analysis of the knowledge revealed by the teachers, it was based on the theoretical model of the Specialized Knowledge of the Mathematics Teacher, the MTSK. For data collection, a document was prepared containing questions about their education, professional experience and their understanding of the Theory of Numbers, for the characterization of the participants and another, containing six questions about concepts related to the Fundamental Theorem of Arithmetic, which were answered by the teachers. Subsequently, a semi-structured interview was carried out with each professor, intervening in the records previously carried out, seeking to analyze the understanding of elements such as the concepts of multiple and divisor, the uniqueness of decomposition into prime factors and the use of this representation in internal and external contexts to the central theme. The results indicate that some of the participants have difficulties in defining multiples and divisors and most did not recognize the uniqueness of the decomposition into prime factors. Furthermore, the properties arising from this representation are little considered for the decision on the divisibility and multiplicity of an integer, with the dominant strategies being the use of the division procedure with zero remainder and the divisibility criteria. It is believed that the results disclosed here brought an important contribution to the scope of studies related to the Fundamental Theorem of Arithmetic